My rankings in order:
FFIV
FFVI
FFVIII
FFT - Excellent job system, political storyline
FFVII - Good storyline, emotional scenes
FFI
FFX - Beautiful, fun "old-school" battle system
FFIX - Good game, even better if familiar with FF mythology
FFV - Awesome job system, odd storyline
FFII - Nice storyline, but junk leveling system
FFIII - Not bad, just less memorable, decent job system
FFMQ - Why did I buy this in '92 instead of FFIV?
I was raised on Final Fantasy. When the first one came out, it was incredible. I was used to Dragon Warrior's solitary quest, but FF's party of four introduced variety in killing monsters. It hasn't aged well, but for it's time, it was one of the best games on the NES.
The SNES age of RPG's has a special place in my heart. The characters were no longer two-dimensional (even if the graphics were). The developments were memorable: Kain's betrayal(s), Golbez trying to use Holy (or White), everyone having sidequests in VI. For me, IV edges out VI because I like the story better and I like having five specialists on a team instead of four magic-using warriors (though Genji Glove+Offering is disgusting).
FFVIII probably touches me the most because of how Squall grows as a character. His change isn't as explicit as a Dark Knight into a Paladin, but he subtly climbs out of his shell. I actually like exploiting the junction system. If you've played through the game before, you can easily become a powerhouse early and breeze through at level 11. It's better on PSP, though. Play some cards, watch Price Is Right, mod those cards, etc.