I've played almost every FF all the way through. Here are my short reviews of them all.
FF1: The start of it all. You have to play it out of respect for what it's done for the entire face of gaming today. The story is okay, but I like the whole death/rebirth cycle that it introduced.
FF2: This game had a pretty interesting story, actually, and it's pretty easy to get into it. The only problem was that leveling up was ridiculously difficult and was really only best done by "cheating" the system. Props for innovation.
FF3: DAMN! This game was GOOD! It pushed the limits of the Famicom to the max. It truly introduced the job system to Final Fantasy, and Light and Dark must join together to defeat the void. Very good game, it's deceptively easy up until the very last dungeon, which is much more difficult than the rest of the game.
FF4: To be honest, I have no idea why this game is revered as much as it is. The story is a lot like Star Wars, and pretty much EVERY character "dies" but they really don't. It's really fucking annoying.
FF5: Ahaha, evil trees be destroyin' the world, yo'. This game had an AMAZING battle system and innovative job system for its time, but its story was pretty cookie-cutterish and predictable.
FF6: FF6 is really enjoyable and has a very interesting story, but the thing that I disliked about it was how you have to gather characters at a certain point in the game. Many seemed almost completely extraneous. Also: if you don't know what you're doing with Shadow...fuck that shit.
FF7: To me, this game is the pinnacle of success. Final Fantasy VII is what brought RPG's truly in the limelight. It had an amazing story, memorable characters, and it really captured the "feel" of being confused and not knowing what to do which parallels reality. I think that's what it comes down to. FFVII was able to make people connect on a deep emotional level because it presented reality through its characters so vividly. I'll agree that it's overhyped, but it's overhyped for a reason.
FF8: Final Fantasy 8 had a really fun battling system (although part of the junction system made it a detriment to use magic, but whatever...that's another story for another time.) I thought the story was pretty good until the third disc or so, if I remember correctly. REALLY good soundtrack and addicting card game.
FF9: This is the only one (barring 11) of the main FF series I haven't completed for some reason. (I would always just get to the second continent and stop, nfc why.) Now my discs aren't good enough to use anymore, and I don't own a playstation. So I can't play it, but I'll get through it one of these days. It has an AMAZING soundtrack (Frontier Village Dali, anyone?)
FF10: This game was REALLY good. I replayed it recently to see where the hell it went wrong because I was pissed off after I beat it the first time. Up until the major "plot twist" (which really came out of left field, if they left it out, the game would still have been really amazing, better imo.) It had a fun battle system, a good story, (decent) voice actors, and memorable characters.
FF12: This game had a fun battle system, but the story wasn't very good. The game was just way too linear for my tastes, and the only real side quest you could do were collecting summons and fighting bounties, which just took too long in general and weren't that rewarding. (Gilgamesh was full of nostalgic win though.) The grinding of some bounties were just ridiculous.
FFTactics: Amazing game, #2 in the series to me. Taking from Tactics Ogre's battle system, FFT sported an amazing job class system and story line. After you got into the game, it was extremely hard to put it down (unless if you kept fucking up a battle and became frustrated.) I made it all the way to Gafgarion in chapter 2 before I learned how to change classes. It has a pretty steep learning curve at first, but the amazingness this game brings is worth it. Truly an amazing game everyone should pick up some time.
FFMystic Quest: Ahahaha, yes, I've played FFMQ. It's pretty terrible, isn't anything like a FF game, and the battle system sucks, but it has a place in my heart for the nostalgia it induces to me.
Ranked:
FFVII
FFT
FFVI
FFX/FFIII
FFV
FFXII
FFVIII
FFI
FFII
FFMQ
FFIV