Outside of the well known ones like Dancing Mad, Suteki Da Ne, You're Not Alone, etc. these are some personal favorites:
FFVI - Esper World : Uematsu is really good at making tracks that sound otherworldly, and this is the peak of that. There's melancholy here, for the fate of the Espers, as well as a rising tension, as obtaining the magicite from Espers is key to which sides wins the war.
FFVII - You Can Hear The Cry of the Planet : Might be the most haunting track in the series, played inside the dead and forgotten City of the Ancients, leading up to Aerith's death. This song is mourning her coming peril.
FFIX - Black Mage Village : This song is really fun and perfectly fitting to the inhabitants of the town. The black mages have only known life a short time, and will only live a short time, they don't have the time/means to learn "proper music", so the track is a mishmash of sounds as they go about figuring what sounds good. Really love the chocobo chirps representing the baby chocobo they hatch and raise.