Here's a curve ball for you:
Final Fantasy VIII is my favorite. HA!
Honestly, it is. I like the characters the most, the world the most, and the gameplay the most out of all of them. Yeah, I'm weird like that.
I've never actually heard of FF fans hating X. They always say it's the best out of the series. I disagree (see above), but I did enjoy it--and X-2 for that matter (Okay, yeah...this guy's insane. I know you're all thinking that now)
IX was all right, but not really my cup of tea. I've only played it once.
FFVII holds a special place in people's hearts--mine included--which is why it is so popular. There are so many reasons people defend that game, and I'm sure you've heard them all: Great story, memorable characters, amazing battle system, first 3D JRPG in the West, first RPG people ever played, Sephiroth, great music...
And then, of course, there is the list of reasons why people hate it: Horrible plot, cliche characters, materia was too confusing, graphics were bad, the typos were painful, stupid Emo Cloud, Aeris nagged, Sephiroth is a cardboard villain...
The list goes on for both sides. Personally, I think it's an amazing game.
XII I did not like because, to me, it screwed up what makes a Final Fantasy game: The characters. None of them were special. Everyone could use everyone else' weapon or skill, you never really got to go find out the backstory of any of them (I'm referring to how you could go on entire quests in the other games to learn about the characters) and none of them really had any real character to them.
Also, I know many people loved the gambit system, but I felt there was a serious problem when I could put the controller on the floor and the game would play itself and not need my input.