Star Trek Odyssey
There are innumerable intelligent species in the galaxy, and characters can be from virtually any of them. If the species you want is not listed here, invent it, and the GM will say yay or nay. Most, but not all, Starfleet personnel come from Federation member planets. If your character is not a Federation species, come up with a creative reason why your character is on board the ship.
Common Federation Species
Other member species include Algolians, Arbazan, Arcadians, Ardanans, Ariolo, Benzites, Bzzt Khaht, Caitians, Coridans, Deltans, Efrosians, Grazerites, Hekarans, Ithanites, Kasheeta, Peliar Zel, Rigellians, Risians, Xelatians, Zeranites, and more.
Some Non-Federation Species
Innumerable other intelligent species exist. Make one up!