My favorites would have to be (in chronological order): III, VII, VIII, and X.
FF3 was just plain fun, and had a pretty solid storyline and neat characters.
FF7 again had great characters all around, including the villians, namely the Turks and Sephiroth.
FF8, to me at least, had a storyline that was simple yet interesting. I really liked that we got to see that Squall's act as tough lone-wolf for what it was, and everyone had their own personality. The graphics were good (though some of the character renditions are cringe-worthy by today's standards), and the CGI scenes were amazing, especially the opening sequence, beach assault, and end sequence. The only real drawback was the lackluster combat/magic system, and while the Junction system was neat in theory, the application made it too easy to power-twink your characters. Though it was nice that you weren't unduly penalized for not completing the assorted sidequests by means of the later boss fights becoming a lot harder because you didn't have the all the "uber" weapons, items, and or secrets. It's probably the overall lack of challenge that makes this one not as popular as other titles in the series.
FFX was graphically beautiful, and the inter-party banter and dialogue from all the characters was a fun touch. The overall story was well-done, and had (for me at least) some very neat twists that I wasn't expecting in the slightest when first playing through. Too bad FFX-2 had to be a horrid "Charlie's Angels" rip.
As for FF6, none of the characters really struck a chord with me, as they all felt too "archetypical," in that I could pretty much predict how they "developed" through the story. That and Kefka had to rank among some of the lamest villians in video games.
A lot of gamers in my area rave about FF9, but while the gameplay was good (much better than FF8), the only character I even remotely liked was the little black mage.
I've got a demo disc for FFXII (came w/ Dragon Quest VIII; fun game btw) that I still need to try out. Here's hoping it's a good one...