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).