Easily IX. Even though, as far as games go, others have had better leveling mechanics, skill learning systems, and more interesting bosses (almost no boss in IX requires any strategy beyond "hit it with the most powerful attacks you have, and don't die", save for the one 'Revive kills Zombie' boss).
IX just has the best story (sorry fans of VII, but your story is too much of a cluster-fuck for me) that grabs you almost immediately with lovable interesting characters who are all emotionally grabbing in there own way. Yes, even Quina. The story has already been summed up in this thread, but really, reading it like that doesn't do it justice. There's a lot more to it, from the way all the lines are written, to the animation on the cutscenes that really convey all the emotion in the cast. The very first time you meet ViVi, for instance, he gets knocked on his ass after being overwhelmed by the size and scale of the kingdom of Alexandria. Before you get to control him, or hear (or rather read) him say anything, the animation has already conveyed his personality.
Similarly, the main protagonist, Zidane, is almost impossible to not like. Unlike Cloud and Squall who are both "I'm a moody angsty ball of quiet rage with loads of unanswered questions", Zidane is a lovable rogue. He's a thief, set out to kidnap a princess, his outlook on life is optimistic, and he genuinely cares about those he finds himself stuck with, even though realistically, he should have no reason to.
IX is just generally full of memorable, entertaining moments, that, even though the cast are caught in a world that through the course of the game lurches from one bad thing to another (by the end of the game, pretty much every city has had some bad fortune or another, almost everyone's been affected) yet the game still keeps Zidane's optimistic demeanor, and despite being an incredibly dark story about a mad arms dealer who's out to conquer/destroy everything, it never feels dark.
IX doesn't usually get as much love for it as some of the other FF's, which is a shame, as it's an under appreciated gem. It may not be as innovative or as creative in terms of gameplay as some of the others in the series, but it's simple nature does it a blessing, as it allows the story to carry it, something that it does with ease.
