Which one? Generally a sans-serif font, although the PSP/iPhone versions use a serif font.
As for a specific font, up through at least Final Fantasy XIII, they used a custom bitmap font to the best of my knowledge. I suppose Final Fantasy XIII could be using an actual type face, but I don't know what it is.
Or did you mean the Final Fantasy logo itself? To the best of my knowledge, that was created by Yoshitaka Amano and isn't any specific font.