My personal favourite Final Fantasy. This was the first to appear on the SNES, released at the same time or just after the console. It featured great graphics and music, rivaled only by Actraiser, and for me at least this game was the selling point for the system. I've played the whole series up to now (discounting the second half of Final Fantasy VIII because the game fucking sucks), and I believe this to be the best.

I think the greatest part of Final Fantasy IV is its distinctive characters. The only other game that can claim this is Final Fantasy VI, and even with that one it's less so. Here, each character is bound to a class, and is pretty much stuck with it. You won't see a fighter-type character using magic, like in VI, or a single character being able to do anything and everything, like in Final Fantasy V/5 (and, to a lesser extent, VII, VIII). Each character's personality also relfects their class. Yang, a monk, is honourable and humble, whereas Edward, a bard, is a whiny ass, cowardly wimp.

One might say the downfall to this is that the characters become boring; with the exception of only two (Cecil and Rydia), the commands and abilities that the characters start with are the same throughout the game. In any of the other games, this would be true. Final Fantasy IV combats this by always having a very dynamic party. Characters come and go constantly, so you don't really have time to get bored of them. And when they come back, it's like meeting up with an old friend. Another condition here is that you're forced to use the more useless characters. Again, though, I don't think this is a bad thing. It forces you to try to do things to compensate for their weaknesses, thereby getting more into the game. Compare this to Final Fantasy VI, where at the end you have a veritable army to choose from, but only ever really use the four strongest.

The story is significantly better than that of the games that came before it, but is somewhat overshadowed by Final Fantasy VI, and perhaps at times VII as well. It definitely blows V out of the water, though.
In terms of weight and tone, it is darker than Final Fantasy I,III,V,VII,VIII, and IX, brighter than VI, and radiant when compared to Final Fantasy II.
One thing it has going for it (debatably) when compared to the newer games is its single story arc. Side quests are shorter and fewer, so usually everything you do is there to advance the plot. Without getting in to it too much, some cool story elements (spoilers?):

In addition to being the first of its kind on the SNES, Final Fantasy IV has several milestones in respect to the series. First and foremost, it has the largest party size of any game: five. All others have four, or a dismal three. I really, really don't know why; the more the better is definitely true. Perhaps console hardware restrictions, or maybe it's harder to balance the games out when there're more characters. Anyway, it's very noticeable. The final party is the best of the series: Cecil Harvey, a Paladin; Kain Highwind, a Dragoon; Rosa Farrell, a White Wizard; Rydia, a Caller and Black Wizard; and Edward "Edge" Geraldine, the Ninja. With only four characters at a time, it would feel... off.

I just mentioned balance above, and that's somewhere that IV really shines. I don't think I'm being presumptuous by saying that it's got the best balance of any game in the series. In Final Fantasy VI through IX, it's too easy to become insanely powerful. Just find the right Espers/Materia/Guardian Forces/etc., equip them to the right character, and BAM, instant demigod. In contrast, Final Fantasy I through III forces you to constantly level up to cope, with II being the biggest culprit (that's a topic all it's own, wow). The two black sheep here are Final Fantasy VIII, where leveling up is almost unnecessary and beside the point (in a bad way), and V, where leveling up is hard to do because the enemies give you almost nothing for experience. In IV, you rarely need to spend too much time gaining experience. The game maintains a constant difficulty; most bosses will take a little work to beat, especially in the hard-type version of the game. However, it's not frustratingly labourious. And, on the opposite end, your party does not become some invincible army dealing out charred, bleeding death by the end of the game. Oh yeah, and there's no time spent trying to learn stupid Blue Magic, or the seemingly infinite number of Rages in Final Fantasy VI, or mastering classes in V and III.

Back to the milestones. Real-time battle made its first appearance with Final Fantasy IV, and Squaresoft really got it right the first time. It would have been easy to screw up. You know it's good because it's not very noticeable; the game still feels like it's turn based.
Dwarves made their second appearance in IV (Lali-ho!). This probably isn't that big of a deal, because they weren't that popular and stopped appearing after V. Their tanks were cool, though.

Second best ending of the series. Best goes to Final Fantasy VI. Honourable mention: Final Fantasy VII, at the final one-on-one Cloud vs. Sephiroth battle. Very cool ass-kicking action there.

Lastly, the talk made about the differences between the English SNES and Japanese SNES game is mostly just noise. Yes, we did get the easy-type version, with missing commands, items, blah blah blah. No, this isn't that big of a deal. And no, the translation, while not great, is not bad either, especially by Final Fantasy standards. And just to set this to rest too, there is no way to revive Porom or Palom in the hard-type game, no white dwarf room or Basilisk's Eye, or anything like that. Apparently Squaresoft is releasing a Final Fantasy IV-Chrono Trigger combo game - a very awesome combo if there ever was one - on the Playstation called Final Fantasy Chronicles. Play this for the full, official, english hard-type game.

Here a few character writeups I did last year when I was very very bored: