Chrono Trigger (SNES, 1995)

Chrono Trigger (1995) is easily the best of Square's non-Final Fantasy games, and one of the finest RPGs of all time.  The game takes place in the year 1000 AD, and a young boy named Crono is going to a fair in celebration of the 400th anniversary of when his country, Guardia, won the war against the fiends, a race of monsters who now live on another continent.  At the fair, Crono runs into a girl named Marle (who is revealed to be a princess) and the two of them hit it off immediately.  They go up to the square where Crono's friend Lucca, a young scientist, is revealing her new invention, a transporting machine.  When Marle volunteers to try it out, something goes wrong and the machine opens up a wormhole, which she is engulfed in.  Crono rushes after her, and finds that he has been sent back in time 400 years.
It is the middle ages, during the war against the fiends, and Marle has been mistaken for the kingdom's queen.  The real queen had been kidnapped, and since the search was called off once Marle was found, this causes a butterfly effect.  Marle is erased from existence since the queen, her ancestor, had perished along the timeline, undoing generations of family lineage.  Crono and Lucca (who has since developed a way to control time gates) are joined by Frog, a knight sworn to protect the queen of Guardia, and they set off to rescue the real queen.  As a result, Marle is brought back.  Upon returning to 1000 AD however, Crono is arrested and found guilty of kidnapping the princess, and in escaping, the kids find another gate which takes them to the year 2300 AD.
The future is bleak, as endless dust storms rage across the planet, and obliterated cities decay in ruins.  A barely functioning computer module shows surveillance footage from 1999 AD, the Day of Lavos.  Lavos, the harbinger of doom, erupts from the planet's core and rains destruction upon the high-tech civilizations of the world, annihilating everything.  Humanity has been barely surviving for the 300 years since this apocalypse.  The kids decide to use their time travelling capabilities to stop Lavos and save the future.
This somewhat lengthy opening to the game offers an ingenious tutorial on the rest of the game's mechanics.  These are the butterfly effect and decision making.  By interacting with the past, you can alter the course of history and change the future.  Decisions you make in the various time periods can have a positive or negative effect on history.  For instance, you may interact with several people at the fair where you meet Marle, and the actions you take will effect how the trial goes.  Likewise, the things you do throughout the game will impact the overall ending you get, of which there are more than twenty.
Worry not, for this game is also as packed with action as it is with intelligent decision making and time-travel.  Unlike its counterparts of the Final Fantasy series, battles are not random encounters.  Enemies can be seen in all regular environments, some minding their own business, some actively attacking you, and can be avoided or faced head on.  Also unlike Final Fantasy, going into a battle will not take you to another screen. Battles occur wherever you happen to be, and the environment can have an influence on the way these fights go.  Each character has a regular attack, and a set of techniques (which use individual Tech Points, similar to MP) to deal extra damage.  Characters can also combine techniques, such as the cross cut with Crono and Frog, where they both slice through an enemy.  Some techs allow you to attack multiple foes.
The combination of fantasy and science fiction elements would become a trend in almost all future Square games, and nowhere does it make more sense than in Chrono Trigger.  Time periods range from the prehistoric era to antiquity, the middle ages to modern day, and the post-apocalyptic future to the end of time.  Every character is fleshed out and brilliantly written in this game.  Every one has a unique personality and backstory, something that was rare in games of that era, and still fairly scarce today.  There are very little negative things I have to say about this game.  It speaks to me on an intellectual, emotional, even spiritual level at some points, something I cannot say for many other pieces of popular media.  It may be a perfect video game experience.

Final Fantasy VII (Playstation, 1997)

For the first time in series history, a Final Fantasy game was released on a non-Nintendo console.  Square was planning to release Final Fantasy VII on the Nintendo 64, but when they found out that the system would still be using cartridge-based hardware, they reconsidered.  The two-year-old Sony Playstation looked like a far better option, since it used CD's for its games, which offered more storage space to make a bigger game.  Even with that additional room, the game spanned three discs.  Well worth it though, since Final Fantasy VII was the most massive and ambitious Final Fantasy game at the time, and my personal favorite.
The story centers on Cloud, a pessimistic and anti-social ex-member of SOLDIER, a military force of the totalitarianist government, Shinra.  He joins a terrorist group called AVALANCHE, led by Barret, who blow up energy reactors in the city of Midgar.  These generators, called mako reactors, are using the planet's blood (or lifestream) for electricity.  Cloud doesn't care about their eco-extremist views, he is only interested in payment for his services.  After a successful bombing of one of these reactors, AVALANCHE regroups at the bar run by Cloud's childhood friend, Tifa.  She provides some of Cloud's motivation, since he made a promise to her (when they were children) that if she needed a hero, he would be hers.
Attempting another bombing, AVALANCHE is caught by Shinra, and attacked.  The attack separates Cloud from the rest of the group, and he encounters the flower girl, Aeris (Aerith in Japan).  Not long after meeting her, he has to protect her from police who wish to abduct her.  Cloud finds out that this is because she is the last living descendant of the Ancients, a race of magical beings who came to Earth seeking refuge, but were met with discrimination and then, extinction.  Cloud comes to fall in love with her over the course of the game, before one of the most famous moments of this game.  Cloud and Aeris manage to regroup with AVALANCHE, but not before Shinra attacks their hometown and base, killing every member but Barret and Tifa.  They decide to retaliate by attacking Shinra headquarters.
This attack is a failure, and they are captured and put into holding cells to be later executed.  Before the execution, however, some mysterious force has destroyed large portions of Shinra HQ, allowing Cloud and friends to escape.  The assailant is revealed to be Sephiroth, former leader of SOLDIER, and long thought to be dead.  He came there to liberate Jenova, a malignant genetic experiment, and his mother.  Sephiroth wishes to summon a meteor to blow a hole in the Earth large enough for him to merge with the lifestream, allowing him to become a god.
Such a lengthy explanation of the plot is necessary to explain the game's revolutionary play mechanics.  The new system for customizing characters is Materia, magical spheres that can be equipped to any character's armor or weapon to grant them its ability.  Materia exist for all skills, from magic spells to summons to statistics boosts.  As you battle, you gain experience points, which are attributed to characters and Materia.  They may level up, multiply, and be conjoined with other Materia.  Similar to Magicite from Final Fantasy VI, Materia allows any character to learn and master any skill.  They also play into the story.  Materia come from the lifestream of the planet, and it a Black Materia that Sephiroth plans to use to summon meteor.  The only thing that can possibly stop meteor is the White Materia, which only Aeris can use.
Battles have also been re-imagined.  For the first time, your party can only be comprised of three characters.  Another first is full-3D modelling for battles (normal environments use pre-rendered backgrounds, similar to matte paintings in old movies), and limit breaks.  Each character has a Limit meter that fills as they take damage, and when it is full, they may use a variety of character specific attacks and skills.  Most of Cloud's limit breaks involve dealing heavy amounts of damage to enemies.  Most of Aeris's are defensive moves, such as healing HP for all characters.  Limits would become a mainstay in the series, though it would be re-named in a few instances.
Final Fantasy VII has received much praise over the years, which has recently turned into backlash.  Many die-hard fans consider it to not only be the best game in the series, but in all of video gaming.  I think that like movies, determining which title is the "best" is impossible because of how vague a statement that is, and how difficult it is to compare games of different genres and generations.  I don't think Final Fantasy VII can be called THE best game of all time, but it is one of the most important.  It was the first RPG to be both a critical and commercial success in the United States which would turn the genre and Square Soft into industry giants to this day.  Its themes of environmentalism, terrorism, fascism, poverty, and even religion are handled fairly well given the atmosphere of the time it came out (we still have trouble talking about these things today).  In spite of all of the worshipers and detractors of this game, it can be considered one of the best video games ever created, and a fitting end to the golden age of Square Soft.

Final Fantasy VI (SNES, 1994)

Just like Final Fantasy IV, this game was re-titled for its North American release.  Fans of the series grew up knowing this game as Final Fantasy III, blissfully unaware that it was actually Final Fantasy VI.  Regardless, it is a some kind of blessing that we DID get this game, because this is the most fully realized, ambitious, and enjoyable RPG of the 16-bit era.  Long time fans of the series argue that either this game or Final Fantasy VII is the best of them all, and those who pick this game have some fairly strong points.  It is the last title to be 16-bit, the last to be on a cartridge, and also the best of them.
This game starts by gracing us with one of the most iconic cinematics of the era, showing Terra, a brainwashed girl, and two empire soldiers riding their mechs (bipedal tanks) across the desolate snowy wastelands to a small mining town, with the intention to steal the crystals.  Terra somehow manages to break free, and is saved by a thief named Locke.  He encourages her to join the resistance group he is a part of, led by the flirtatious king of Figaro, Edgar, and also includes his estranged brother, Sabin.  They discover that the Emperor is collecting these crystals, called Magicite, to try and harness their magical powers.  It is revealed that long ago, humans could use magic, but lost this power due to their recklessness and technology.  The Magicite is actually the incarnation of a dead Esper (formerly known as summons) who come from another realm.  The Emperor is being influenced by the maniacal general Kefka, who wishes to harness all of the Esper's power for himself, to become the new god of magic.
Final Fantasy VI is epic in all regards.  The interpersonal relationships the playable characters have adds much emotional depth and weight to them (and there are a lot of them).  This is the first time a Final Fantasy game used a steam-punk aesthetic instead of the typical European renaissance style.  This allows many creative visuals of a post-apocalyptic world where European architecture and futuristic machines conglomerate together.  The visuals are always clashing, and always eye-pleasing.  The Super Nintendo was already known to have the best graphical prowess at the time, but this game pushes all of its power to the limit.
Terra is the very first female lead in a final Fantasy game, and she is still the best one.  She (and every other character) is written very well, with human traits and great dialogue.  She is a target of the empire because she is one of the few living people who can naturally use magic.  This is because she is actually a hybrid of human and Esper.  To stop Kefka from destroying all of existence, they must seal the portal to the Esper's world, which runs the risk of killing Terra in the process.  Speaking of Kefka, he is arguably the series' best villain.  He is a twisted, sick, demented, and vile human being.  He ruthlessly kills and destroys with fetishistic delight, understanding nothing but hate.
To compliment the incredible story and characters, Final Fantasy VI has one of the series' best systems for customizing party members.  Each character you add to your roster has their own person-specific abilities, such as Sabin's blitz moves or Edgar's arsenal of tools.  When you collect pieces of Magicite, however, you can equip them to any party member, and as they gain experience from battles, that Magicite levels up and imparts some magic and summoning abilities to them.  Just like Final Fantasy II, with some patience and resolution, any character can learn any skill.
Final Fantasy VI is most likely the RPG that Square had dreamed of when they made the original game.  It is the most realized and epic of all of the 2D Final Fantasy games.  The story reaches heights which video game storytelling had previously never imagined, with its emotionally charged characters and plot.  Consider the opera scene where Celes, an ex-general for the empire, is made to stand in for the ill-fallen singer, and the lyrics of her song actually reflect her concealed love for Locke.  The music adds so much dimension to this game, perfectly matching every mood and scenario of the story.  This would be the last time a Final Fantasy game would be released on a Nintendo console, but oh, what a way to go.

Final Fantasy V (Super Famicom, 1992)

Part of the reason why half of the retro Final Fantasy games were not released in the United States was because at the time, RPGs were a fairly niche genre which most American gamers were not accustomed to.  Releasing one of these games was a fairly big risk due to the cost of localization.  RPGs contain a relatively large amount of written dialogue and text, which is expensive and time-consuming to translate from Japanese to English, especially if the game is not expected to do well in sales.  Even the well-known Final Fantasy series was not invincible to this, and Square's next installment, number V, was the last of these games not to be released in North America.
Final Fantasy V follows Bartz, Lenna, Galuf, and Faris, a group of people who are brought together after a meteorite crash causes the four elemental crystals to lose balance (notice any themes in these games?).  These crystals form a seal on the evil sorcerer Exdeath, who wishes to destroy the world.  This game has, admittedly, one of the weaker stories in the series, but is made up for by its characters and gameplay.  Unlike other Final Fantasy games, V does not take itself as seriously and features more humorous scenes of character interaction.
This game revives and perfects the job system.  The greatest thing about this game is its amazingly deep character customization.  There are some new classes added, such as time mage and berserker, but the way you are allowed to every class is astounding.  Like Final Fantasy III, you may change character jobs at any time, and level them up in battle by collecting experience points and ability points.  New to this game though, is how you can combine classes.  Each time a class gains a level, the party member learns a new skill which they never forget, and if you change classes, you can equip one of these skills to the new class.  This allows virtually no limit to the party configurations you can devise.  You can have warriors who use time magic, red mages who can summon, magic users who can use swords, etc, etc.
Battles are, in all other respects, identical to Final Fantasy IV.  The active-time system is back, which is probably the best battle system the series would ever have.  It would stay in until Final Fantasy X on the Playstation 2, but popular belief suggests that the series had begun to slide downhill by that point.  This fifth game's perfection of the job system is enough to make it stand apart from the rest, regardless, and keep it held high as one of the best Final Fantasy games.  It is remarkable that even at five games, the best still had yet to come.

As a side note, all three of the Japan-only Final Fantasies have received ports on American systems retroactively.  Final Fantasy II is available on Final Fantasy Origins on the Playstation (which also includes Final Fantasy I), and on iOS.  Final Fantasy III was first released stateside on the Nintendo DS.  Final Fantasy V is available on Final Fantasy Chronicles on the Playstation (which also includes Final Fantasy VI).

Final Fantasy IV (SNES, 1991)

Final Fantasy IV was the first game in the series to be released on the brand-new Super Famicom and Super Nintendo systems, making it the second North American Final Fantasy game.  Because there had been no Final Fantasy II or III in the States, Square decided to rename this game Final Fantasy II, hoping that it would avoid confusion.  I actually own this copy of the game.  This is the most re-released installment in the series, having been ported to the Playstation, Game Boy Advance, Nintendo DS and more, and for good reason.  Final Fantasy IV is one of the finest games in the whole franchise.
The game stars Cecil, captain of the Red Wings, the airship armada of the kingdom Baron.  He has orders to collect the elemental crystals, slaughtering innocents along the way.  Racked by the guilt, Cecil gains the courage to speak out to the king, and question his motives.  The king relieves Cecil of his post, and when his friend Kain tries to stick up for him, he is also dismissed.  Cecil is left with a package to deliver to the valley of Mist, and upon reaching this town, the package reveals to be a bomb which burns it to the ground.  The only survivor is an orphaned girl caller, Rydia.  Startled she calls a Titan which causes an earthquake which separates her and Cecil from Kain.  Cecil eventually discovers that Baron is being controlled by the mysterious Golbez, and his four fiends.
I could fill this entire article with a plot summary about this game, which is one of its best defining features.  Final Fantasy IV is the first game in the series to feature a fully realized plot with deep, interesting characters, twists and turns, and a genuine feeling of weight to it.  Characters have relationships with one another.  Cecil is in love with the white mage Rosa, for whom Kain also has affections for.  Rydia comes to forgive Cecil after he protects her from some guards.  There are more characters than I could do justice to, since they are all marvelously written.  Each new hardship the cast is faced with pulls at the heartstrings, aided by one of the greatest musical scores ever composed for a video game.
The game also perfects the gameplay of the previous games, while yet again reinventing itself into something fresh and new.  The biggest improvement is the introduction of the active-time battle system.  The way this works is that each party member and enemy has a time bar that when full, allows them to take a turn.  This makes battles fast-paced and dynamic, more interesting than before.  For the first and only time, your party could hold five characters, and they came and went as the story progressed.  Each character has a job class predetermined for them which is crucial to them as people and the story.  Cecil starts as a dark knight, but by finding his own redemption for his past actions, he may become the paladin.  Characters gain experience for winning battles, and gain new job-specific abilities with each level.
This game benefits immensely from the Super Nintendo's superior hardware.  The 16-bit processor allows more colorful and detailed characters and environments, and exquisitely composed music.  Final Fantasy IV was the biggest game in the franchise yet, in terms of scope, technology, and ambition.  Since no one stateside knew about Final Fantasy II and III, this game was counted as a gigantic step forward.  From the first Final Fantasy, it is an immeasurable step forward.  Compared to the Japan-only entries, it still propells light-years ahead of them, and would begin a golden age for Square Soft titles.

Final Fantasy III (Famicom, 1990)

Final Fantasy III is the last game in the franchise on the Famicom (Japan's NES), and yet another title that American audiences would miss out on.  The first North American release of this game did not come until it was remade in full 3D for the Nintendo DS handheld system.  Regretful, since Final Fantasy III is possibly the most realized RPG experience of the 8-bit era.  Once again, Square Soft reinvented the series, combining some of the best elements from the first two games, and adding some vast improvements to their mechanics.
Final Fantasy III follows four children who find that they are destined to become the light warriors, heroes called by the sacred elemental crystals to fight back the forces of darkness and restore worldly balance.  It is prophesied that this happens every thousand years, and last time there were four warriors of darkness who were called to defeat the overpowering light.  If balance cannot be restored, then the elements of nature will fall into chaos.  The seas will run wild, the earth will decay, the winds will stop.
Upon coming into contact with one of the four major crystals, they are bestowed with small crystals that can grant them the abilities of different job classes.  Yes, Final Fantasy III is a return to the old job system from Final Fantasy I, with some major improvements.  Now you may change any party member's class at any time, and there are many additions to the jobs you have to choose from.  New here are the likes of summoners, dragoons, and blue mages.  There is high incentive to experiment with multiple class variations and combinations.
Some of these jobs are somewhat useless, such as the viking class which is too similar to the superior warrior class to be of much use (the only difference is they use axes).  The additions that are original are some of the most powerful in Final Fantasy though.  Summoners are a must-have in the party.  They may use the brand-new summon magic, which calls holy beasts to fight alongside you, often dealing massive amounts of elemental damage.  These summons, interestingly enough, come from the lore of Hinduism, Judaism, and Islam.  Blue mages may learn bestial abilities, which, with some patience, can be helpful.  Dragoons are swift fighters who can use jump, which makes them temporarily invincible, and then they deal massive damage after two turns.
One of the most refreshing improvements to this game are how the sins of the previous games were completely removed.  Ineffective hits are a thing of the past, since now, when a party member is about to attack a felled enemy, they intelligently move on and attack the next living thing.  Back is the charge-and-level system of magic, but it is easier to use now that there are magic-restoring ethers in the game, and levels of magic are allowed to have charges in the double-digits.  Once again, experience points are earned for defeating enemies, but not only do they go toward building general character statistics, they go to building class levels.  The higher your class level is, the better you are at their skills, and changing jobs will not remove any of the experience you gain.
Like the previous games, Final Fantasy III is not perfect, but can be counted as a major improvement to the series as a whole.  Its weakest point is its story, which is not very cohesive throughout the game, plus the story can get repetitive, and fails to carry as much weight as Final Fantasy II.  The strength of its gameplay alone makes up for this though, since it allows more customization than ever, and offers enough incentive to keep playing just to experience more powerful jobs and build characters.  The only direction Final Fantasy had to go from here was up.

Final Fantasy II (Famicom, 1988)

The first Final Fantasy game did well enough that exactly one year later, Final Fantasy II was released, only in Japan.  Since the first game tied up its story tightly, Square felt no need to make II a continuation of its story, so they decided instead to make it a completely original game.  The story of Final Fantasy II follows four kids who are orphaned in an attack on their hometown by the wicked Empire.  The Emperor has opened a portal to a world of monsters and is controlling them in a plot for world conquest.  One of the kids, Leon, is separated from his friends, Firion, Maria, and Gus, and the three of them join a rebel faction.
This is actually one of the better plot-lines in the Final Fantasy series, due to the way it is told throughout the game.  The centerpiece of the story is the war between the Empire and the resistance, and it does a marvelous job at making it feel like a war.  There are some genuinely sad moments when characters you've known and fought alongside with die.  Yes, this is the first entry in the series to feature themes of death and war.  For one of the less-played and discussed titles in the series, it also introduced a few things which would become standards in all titles to come.  Final Fantasy II introduced Cid, here an airship pilot who runs a ferry service.  In all of the following games he would have something to do with airships (with a few exceptions).  Also introduced are the Chocobos, giant birds that will carry you across the map if you are lucky enough to stumble upon them in the forest.
Final Fantasy II improves upon everything in the first game (despite still holding a few flaws like ineffective hits).  For the first time in the series, the story and characters were the focus of the game.  Every character you encounter has a personality and back story that weave into the plot.  There is a significant amount more dialogue here than in the first game.  Another thing that is improved is the battle window and graphics.  The first game had a revolutionary side view of the action (most RPGs at the time used a first-person view) which showed each character in your party and every enemy, with stats on the side.  There was very little animation due to the low budget of the game.  Final Fantasy II reduces the clutter by placing all of the information at the bottom, and now every different action has a different animation.  Magic users no longer have to struggle with leveled charges, because now each character has MP (Magic Points) which is spent with each spell.
The biggest improvement in the game is the leveling system.  No longer can you choose which class each character will be.  Instead, each character may potentially learn any skill, attacking, magic, and more.  Also gone are experience points, in favor of a new system which takes into account every action you take in and out of battle.  The more damage you take, the more your defense and HP (Health Points) go up.  The more you attack, the better you get at a certain weapon.  The more you use magic, the better you get at each spell.  This system is not hard to cheat though.  You can have party members attack each other to raise HP significant amounts in a single battle.  There is a glitch where if you select an action, and cancel it, the game does not un-count the action from your experience, allowing you (with some patience) to level up attributes of which you did not actually use in battle.
This system is strange to get used to at first, but it actually makes building characters more interesting than in the first game since you can make progress with every battle, and it is more realistic.  The first game featured a heavy emphasis on level grinding to progress, but this game has a much faster pace, helped by its new systems.  The Final Fantasy series likes to reinvent itself with every new installment, and even when a game fails for one reason or another, their constant experimentation is admirable.  If every game were like Final Fantasy I, I doubt the series would have survived as long as it has.

Final Fantasy (Famicom, 1987 / NES, 1990)

"The world is veiled in darkness

The wind stops,

the sea is wild,

and the Earth begins to rot.

The people wait,

their only hope, a prophecy:

'When the world is in darkness

Four warriors will come...'

After a long journey,

four young warriors arrive,

each holding an Orb..."

In 1987, a little Japanese game developer called Square Soft was on the verge of bankruptcy.  With only enough funds to create one more game, they decided to make a fantasy RPG inspired by Dragon Quest and Ultima.  They decided to call this last game Final Fantasy.  And of course it was a massive success, which catapulted Square into the forefront of RPG development for the rest of time.  The game would take another three years to see a North American release, where it received lukewarm praise and sales.

As explained in the opening text, the four orbs that control the elements of the world (earth, fire, water, and wind) have been dimmed by four elemental fiends, and you control a party of four warriors to restore light to the orbs.  The thing that made Final Fantasy stand out at the time was its deep class system which adds a large layer of strategy to the game.  You may select the character class of all four of your party members.  The choices are warrior, monk, thief, white mage, black mage, and red mage.  Warriors have the highest strength, monks can use bare fists (the advantage is not having to buy weapons), thieves have higher evasion and eventually become the ninja class (the strongest in the game), white mages can use defensive and healing White magic, black mages can use offensive Black magic, and red mages can use some Black and White magic, as well as moderate weapon strength.  

The game essentially gives you no sense of direction, meaning you must figure out where you are supposed to go to progress.  You eventually gain vehicles like a sailboat, canoe, and the series-standard airships, which can be used to fly between locations.  Your first objective is to save a princess from the dastardly Garland, and once you do that, the king issues a bridge to be built, and then the rest of the continent is open to you.  Garland will return in the game's climax, in a turn of events which is as original as it is confusing.

The game is still fun to play today (I have completed the original version of the game) but still comes with its flaws.  For one, this game has what are called "ineffective hits".  This is where if you tell two characters to attack the same enemy, and the enemy dies before the other party member gets to attack, when they take their turn, they will swing at the open air and miss.  This happens more often than it should (it shouldn't really happen at all) and causes much frustration.  Another quirk is the magic system.  There are eight levels of spells for each type of magic, with a number of charges that can be used for each spell.  The maximum number of charges is nine, which severely limits how much magic you can use.  The only way to restore charges is to stay at an inn.  Despite these legitimate complaints, Final Fantasy is a great and challenging experience.  Its combination of fantasy, science fiction, and customization ensures that no two playthroughs will be the same, and always enjoyable.