My favourites are III, V and IX. IX most of them but that game will certainly get some votes so I picked III this time.

III, both NES and DS version is an amazing game. The story is so great and deep considering it's time and the jobsystem was a very great thing. Not to mention it did a lot for the series, like introducing moogles, summons, jobs and so much more.
It has a great OST for a NES game ("Aria, The Maiden of Water", "Boss Battle", "Forbidden Land Eureka", "Dark Crystals", "This is the Last Battle", "Eternal Wind" come to mind) and the DS version only improved it. (Especially "This is the Last Battle", "Forbidden Land Eureka", "Dark Crystals", "The Crystal Tower" and "Aria, the Maiden of Water")
And Forbidden Land Eureka, The Crystal Tower and the Dark World (both versions) are some of my favourite Final Dungeons in the entire series.

Overal, a great game, unrightfully put in the shadow of FF II and IV.