Ah, tripping the Final Fantastic... it's kind of unfair to compare the games, because the technology has changed so much, so fast. Here are my own favorites, loosely grouped by time-period:
Best of the early 1990s: FF 4. I didn't run across this until quite recently, actually, but it's impressive how much of the Final Fantasy magic is there. Addictive, immersive, and a great storyline, the multiple plot twists were never forced or artificial. Cecil grew on me as a character, and watching him mature and deal with the very tough legacy of his past was a delight.
Best of the late 1990s: FF 7. Deepest characters and RPG storyline of the 1990s. The visuals have aged a bit, but the underlying story, a kind of late 1990s eco-fable, is dynamite. Cloud, Tifa and Sephiroth - damn, what amazing characters. Certain parts of this game still get me misty-eyed (Aeris! noooooo!!!!). Also remarkable: the amount of subtle humor and satire in the storyline - corrupt politicians, scheming scientists, etc.
Best of the early 2000s: FF 10. Great characters and storyline - yeah, yeah, I know the US voice acting was... uneven. (Yuna's closing speech: *wince*. Say it ain't so, Yunie!). But when the voice actors are "on", it's terrific. Great art design, marvelous environments, sturdy battle mechanics, and a surprisingly deep story about guilt, family and redemption. Tidus and Yuna are magical together. Wish Rikku and Kimahri got more air-time, though.
Best to date: FF 12. Best. Final. Fantasy. Ever. It's that good. Reasons: (1) strong, independent female characters. (2) open-air gameplay and presentation, the gambits system works beautifully. (3) stirring sound-track and some of the finest voice-acting ever performed (both Japanese and English versions are marvelous, but Gideon Emery and Nicole Fantl deserve some kind of Nobel prize for their voice-acting). (4) geopolitics of storyline. Oh, is the story ever complex - layer upon layer of betrayal, intrigue, revenge, Empire, anti-imperial resistance, which builds and builds to the conclusion. It's also the first videogame in history which has a credible interracial/cross-cultural romance at the heart of its story. Just amazing.