Lilties and Yukes from the FF Crystal Chronicles series.

Bangaa, Seeq, Viera, Nu Mou, Gria, and more humanoid playable moogles from FFTA series

Dwarves from multiple previous games in the FF series. Stout people with impressive beards. Yes even the women have impressive beards... >.>

Burmecian from FFIX

Guado and Ronso from the FFX series

Sentient machines - Actually a selectable race in the FF legend series back on Game Boy and also on Chronotrigger

Mystics - Chronotrigger though most kind of just looked like elves

The mushroom people in Secret of Mana.