Gosh, it's so hard to decide for me, because I really like all of them. I don't want to make another wall of text like I just did in the "Least Favourite" topic, so I'll try to be brief.

Like a lot of people here, I'm surprised that FF Tactics wasn't listed, because it was very good story-wise in my opinion. That said, I'm having a really difficult time deciding between FF IV, VI, and IX. For me it's between those three.

IV - I felt that FF IV just had this classic feel in a really good way, which gave it a lot of charm. As Bastian said, it really brought the classic concepts of "wizards, castles, bards, and swords" out, but in a nice way that was very fresh. It also had really nice music, which adds to the experience [everything counts!], as well as nice scenery [considering the graphics of the time].

VI - Even though the graphics were better, the scenery wasn't as nice overall. Still, this game had such wonderful characterization as well as quite a large margin for customization [as FF II did in a different way], which made the game quite fun. Although its story wasn't quite as "epic" as a few of the other Square-titles, it was still presented quite nicely and was also well thought-out.

IX - To me, this one combines a wonderful soundtrack, wonderful scenery, good characterization, as well as a very in-depth, wonderful story. Even though I would've loved to have Beatrix [she's so awesome] instead of that annoying fat rusty pile of tin [yes I find Steiner a bit annoying], I still enjoyed the entire array of characters that integrate themselves in Zidane's path. It also had great villains, and even an entirely new world, as well as the classic "world poison" that is manifested in this game as "Mist", which is a pretty cool concept in itself.

When it comes down to it however, I think I'll have to pick FF IX. For me, this one is just a fine hair above the other two. I know that I said I was going to try and not post a wall of text, but I ended up doing that anyways. Sorry! I tried!