The series has a very strong pedigree, all of them fresh and attempting something new either in the story or in gameplay. I've played most so it was hard for me to narrow it down to 3. Personally I've chosen:
Final Fantasy VII: So special to me as it was one of the first games I'd ever played proper. And it didn't disappoint with so many iconic moments that still live on in the memory. Also, don't mess with Sephiroth.
Final Fantasy VIII: A fair few say it's the worst in the series but I disagree wholeheartedly. There's a hidden depth in that story outside of the romance between Squall and Rinoa that people don't see. I loved the setting, the more realistic approach to the characters, and like Shi, I tended to relate to the cast a lot, particularly Squall. Started off closely guarded and inconsiderate of others but he opens up as the story progresses. I liked the combat too, having to draw all the time was a bit of a grind, even now when playing on the PSP, but I still like it. It's the only FF in which I'd beaten Omega Weapon
Triple Traid still is the best FF mini game. And lest I forget, it also had the best opening. Liberli Fatali
Final Fantasy XII: For me, it's the most impressive FF title. The sheer scale of Rabanastre, and the world of Ivalice as a whole is just incredible. The cast, aside from Vaan and Penelo, were engaging and the political machinations of Ivalice and the faux-Shakespearean dialogue was a fantastic effort of localisation. Without sounding like hyperbole, some of the lines the Judges say was almost like poetry. And you have a great combat system that people say let's the game play itself, but is hugely strategic and removes a lot of the unnecessary grind for you, and some great hunting missions spanned over the world that put the combat engine to the test, with great rewards too and just kept me coming back for more. Unfortunately it might have been too open-ended, so much so that the narrative never really has a grip on you, and if you're anything like me, you forgot about events the more time you spent messing around. If it had something like FFXIII's datalog, then it would have been hugely appreciated. Still, it's epic in every sense.
Haven't completed XIII yet, but I think I've played enough to consider it my 4th favourite. I'll wait and see how the story wraps up before I can tell for sure.