I'm a great fan of the Final Fantasy series, and I love most of the FF games I've played, which are VII, VIII, IX, X and X-2.(Eagerly awaiting XII to reach Europe).

VII: Haven't got that far in this game, because it doesn't really run well on my system.(I had it for PS1, then the first disc got scratched, then I found a copy of the PC version). I just got past the Midgar Zolom, but the game keeps freezing up at this point. Still, what I've tried of this game has been good. The story was surprisingly dark for a Final Fantasy game(this was the last FF game I tried, so I'm judging it compared to the later ones), but I found that to be a good thing. The mood is fantastic. The materia system is interesting, though I haven't been able to try some of the more advanced combos just yet. Perhaps it will turn out to be the most flexible and enjoyable of all FF-character systems.
On the negative side I don't identify that much with the player characters just yet, though I already think Sephiroth is great.

VIII: First FF game I played, and so my opinion on this might be influenced a bit. I love this game, I played through it twice and have recently been comtemplating starting over again.
I didn't really mind the Junction system, I thought it provided a good way to really customize your characters to your hearts content. Drawing magic from monsters might be a bit tedious, but there are easier ways to aquire it, notably item refinement.
I was quite fascinated by the story, though I didn't like the characters that much.
The various secrets were also fun to discover, and the GF's had very nice animations. FFVIII also has my favourite FF minigame, Triple Triad.

IX: IX I have mixed feelings about. It is most certainly the game where I identified most well with the characters(gotta love Vivi), perhaps in part because of the ATE system, and the storyline was among the most fascinating. It also had great humor, something I've missed a bit in the other games. The scene with the love letter mixup actually made me laugh at loud, one of the few times a game has made me do that.
However, I thought the skill-system was a bit boring, and the combat system I found very frustrating, mainly because the actions of characters were delayed quite a bit, which meant that you could ask someone to use a potion on someone near-death, only to have him actualy do it quite a bit later, when it was already too late. Combat was in general challenging, because you didn't have the option of going all-out nova that the other games provide through limit breaks, overdrives or GFs.


X: Also among my favourites. The storyline was great, in my opinion. Voice-acting enforced the personalities of the characters and presented them well, though the characters themselves were not quite as intriguing as those from IX. I didn't really find the voice of Tidus as annoying as many people seem to have. I found Maester Seymour to be a very interesting villain, though I suspect Sephiroth will surpass him when I get further into VII.
Liked the Sphere Grid, liked the new take on summons(though it would have been nice to have had more to choose from), liked the completely turn-based system which was all tactics and no reflexes(aside from Overdrive-inputs).
Was a bit disappointed with the lack of a world-map and the possibility of free exploration, but even so there were plenty of secrets to discover, and it didn't really ruin the game.
Blitzball was fun at first, but became tedious when my team became too superior and each match was basically 10+ minutes of waiting.
My main complaint about X is that it is a bit too easy. The end-boss, for example, was a complete joke.

X-2: I do not believe this game deserves the name Final Fantasy. The storyline and the characters were extremely and utterly annoying. They destroyed Yuna and Rikku here, both of which I quite liked in FFX. In general large parts of the story is just...silly.
That aside, X-2 has some good qualities. There are some nice minigames, notably Sphere Break which kept me occupied for quite a while. The dresssphere/garment grid system was also quite fun and made for some very flexible characters. Trouble with it was that once you had mastered a Dresssphere, you didn't really have any incentive to use it anymore. Also, a lot of abilities on the different dresspheres were a bit too similar.
This is probably the only FF game I didn't really enjoy. The storyline and the characters just ruined it for me.