Final Fantasy V, at least amongst Western fans, is often remembered as the bastard stepchild of the 16-bit era Final Fantasy games. It was skipped over for localization in favour of lesser games, like the eurocentric Final Fantasy: Mystic Quest, and wasn't officially released in English until 1999 as part of a PlayStation anthology.
Even those that suffered through the port's technical issues found that the story and characterizations were lacking compared to both Final Fantasy IV and VI, much less contemporary games. Even its soundtrack, composed by the usually sterling Nobuo Uematsu, was viewed as a bit of a letdown. And yet, amongst longtime fans, Final Fantasy V is regarded as one of the best in the series.
The sole reason for this lies in one of the most fascinating character customizations seen in an RPG -- the Job System. The original Final Fantasy introduced six different classes, and your selections were set in stone from the outset of the adventure. Final Fantasy III (the Famicom one, not the retitled SNES game) greatly expanded that number, and allowed gamers to change classes between battles.
Final Fantasy V went one better and allowed the party members to permanently learn skills while assuming a character class, allowing one to customize their party members with practically any ability. Technically, Dragon Quest III implemented something very similar, but the type of skills found in Enix's games were just variations on your standard attack, status, and buff/debuff skills.
Final Fantasy V goes completely crazy with jobs like Geomancers, where the type of background will determine a special attack, with no MP cost; Samurais, which can toss spare gold for huge amounts of damage; Mimes, which are the most customizable characters and can mimic the preceding character's attacks; and Necromancers (in the 2006 GBA port), which turns a party member into a zombie but allows them a special range of dark art magic spells.
The possibilities for hybrid classes are astounding. Imagine creating a Mystic Knight, who can enchant swords with elemental powers, with the Monk's charge ability, allowing you to delay an attack for a few seconds and unleashing a more powerful attack -- you can totally destroy an ice-based foe for insane amounts of damage.
And you can customize your whole party like this, if you want. If figuring out ways to break the game's balance makes you absolutely giddy, Final Fantasy V is the perfect puzzle. Of course, in order to balance all of your powerful skills, Final Fantasy V is significantly more difficult than either IV or VI. Leveling up through traditional means barely offers any real rewards, so if you get slaughtered by a boss, blindly grinding won't help at all. Rather, it gives you incentives to try out different jobs, explore different skills, and basically just play around to your heart's content.
The Job System does have a few limitations which are a little frustrating. In order to maintain some semblance of balance, you can only equip one additional skill in addition to your current job. As a result, many lesser skills become obsolete -- or even useless -- in lieu of more important abilities. Furthermore, you can't choose which order to learn your skills, forcing you to fight through some of the weaker abilities in order to reach the ones you actually want. Both of these were fixed in the absolutely brilliant Final Fantasy Tactics -- a melding of Final Fantasy V's Job System with Tactics Ogre's strategic battles.