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.