At first glance this is another 'what's your favourite FF' thread. But no! I'm going to force you guys to pick apart what you like about each game and then make some hard decisions.
Here's the deal: which of the three games would you bring with you to a desert island, never to play the other entries again? For example, I wouldn't pick FFVI, as good as it is. Yes, it has an amazing tale to tell (especially by today's gaming standards), but just doesn't present itself as well as VII to me (which makes sense, it being a SNES game). So VII wins out over VI. Now, I could pick both VI and VII, but then I'd have two entries that scratch a similar itch for me, and what about my other itches? As far as the 2D itch goes, there are other 2D entries that can do other things as well - FFV, for instance. Basically, you have three choices and you need to get the most value out of those choices.
So without further delay, here are mine:
FFV: Lighthearted in a very enjoyable way. The most fun Job system in the series. I come back to this game almost more than all of the others (or at least want to but can't find the time). This game scratches the 2D itch and has probably the most satisfying pure gameplay and adventure before the series started getting deathly serious about everything.
FFVII: My choice story-driven entry. To me it has the most interesting of all the FF stories, followed closely by VI and a little less close by X. It's probably the most memorable game I've ever played. It scratches the story-driven itch, and is put over the top by its adventure-game atmosphere, amazing setting, and beautiful pre-rendered backgrounds. VI is its closest competitor for the "story-driven" entries, but doesn't have the same aesthetic appeal.
FFXII: I said V has the best pure adventure, but I think XII comes close or even tops it. It has a wide open, living world that is just a ton of fun to explore. The Gambit system lets me explore and battle and a brisk, non-interruptive pace. It's the most unique in the whole series and a lot of fun to just run around and play. I think it has the most core content of all the mainline FF games (that is, sidequests that don't involve card games, Blitzball, Chocobo breeding, or other stuff that's a completely different flavour as the main game), and that means I can play it longer during a single playthrough than probably all of the other entries. It's also beautiful and glorious and a 3D JRPG done right.
What about everyone else? I'd like to keep this limited to the mainline games: I-XIII, including X-2 and XIII-2. No Tactics series or Theatrythym or Crisis Core or whatever. Just the numbered series.