One of the things that I think really puts FF titles ahead of the rest of the RPG pack is how they catch your attention right off the bat. The stereotypical 'you are just a nobody living a normal life until something special happens' is just about as non gripping as you can get.

6 - FFV
5 - FFVI
4 - FFIV - Seeing the game start right as your distinguished military career was ending was a fun twist.
3 - FFX - I though the opening FMV was super cool. The game was all downhill after getting to Spira though
2 - FFIX - Seeing all the different pieces coming together for the show was an excellent setup. Makes you are jumping into an already vibrant and active world, instead of one that was boring until you started watching.
1 - FFVII - this on grabbed my interest and imagination right from the second the first FMV loaded.