I am only voting for games I have completed. I have not completed FF12 (not even close) and FF1. I have never touched FF2 and FF3. Also, I still have not played FF13-2, but I intend to eventually.
1. FF7; I still consider it one of the greatest games of all time. It might be overhyped, but I still think this game is so superbly made. The entire Midgar section before opening up the huge world was so awesome. The story was so different for me at the time, and mysterious, and dark, with great plot twists and lovable characters (and even enemies). Graphics were such a delight at the time. Music was almost Uematsu's best. Battle system was addictive as addiction can get. I still fully stand by this installment as the greatest of the series.
2. FF9; An extremely underrated game of the series, this one does so many things right. I still think it has the best characters and ending of the series, as well as some of the most charming music in the game industry. I also want to say that I think this installment had the best dungeons...very clever for the most part. The whole thing is such huge, too, and charming in so many ways. So, so underrated.
3. FF10; I know this game has quite a few flaws and drawbacks of the FF series, but I still really, really liked it. I have many fond memories of this. The story was still good to me, and the characters were all right. But what really got to me was the battle system and its sense of progression...I loved the trial dungeons too. It also presented some of Masashi Hamauzu's best music. I also think this one has the best beginning to a FF.
4. FF4; A simple but effective story with a huge mid-way plot-twist that changes narrative direction and even gameplay direction.
5. FF6; I know this is considered by many the best, and it is indeed a great game to me, but when I think back at the most memorable, for some reason, FF6 doesn't scream at me. Maybe it's because I caught it later than a lot of you. I really loved some of the characters, like Kefka, and I really, really loved the world. Some of the dungeons were fun, too, and of course the entire 2nd half of the game was crazy. But I think for me, at least when I played it at that time, it felt like the story took a backseat when the 2nd half opened up, and I was all about the narrative at that point in my life. Now it's different, and maybe if I replayed it it'd be promoted on this list. A really great game, no doubt, but I can't consider it one of the best.
6. FF8; I hate the battle system. So, so, so much. I tried to like it so many times, and eventually, I can usually learn to love. But not this one. It just drove me nuts for so many reasons. I can admit that maybe I just didn't "get" it. I was still pretty young. But as a kid I always thought it was just a bunch of cheap bs. Speaking of bs, the story does some bs plot twists too...but I just love the scenario so much, and the creativity of the world, and the two main characters love connection, that it just pleased me regardless. Also, the biggest reason why this is still up on the list is because this is by far one of the greatest music soundtracks ever.
7. FF13; The story is bad. The characters are bad. The dungeon designs are bad. There are no towns. There really is a lot of stuff this game did wrong, and I consider it one of the weaker installments; however, it still did some things right. The battle system is fantastic and I consider it one of the best in the series. I also can't get over how pretty it is. Despire being lame or overly predictable, there were still some memorable scenes, and Gran Pulse area was great. But man did that ending suck.
8. FF5; I know a lot of people love this one, but I always felt like this was the black sheep of the series. Good game, but again, as a kid, I was about the narrative, and FF5 certainly didn't have that. I barely remember the story, except for negatives. Heck, FF13 might even have a better story. I liked the battle system but I don't swear by it like some of you. I also thought the dungeon design was more repetitive and less creative. Music is fantastic, though, and I did like the amount before-the-final-boss content there was.
9. FF10-2; This is the only FF game that I honestly did not like. Music was sometimes good, and sometimes awful. Story was boring and non-existent until the very end, where it got a bit interesting. Everything felt recycled and not in a good way. I preferred FF10's battle system a lot. This one just didn't click with me.