From what I know here is a list of races
Human (Amarant is confirmed human...which most likely makes Brahne human to...just blue skin disease?)
Black Mage
Summoner
Burmecian (I believe thats the name..Clerya goes under that)
GILGAMESH (He gets his own race)
Hippo (I don't know)
Duck (with the trumpet)
Qu
Genome (a little late)
Monster (not going into detail)
Thats all I can think of