Only some of the PC species in the PHB are available in my game, and Elves and Gnomes are slightly altered.
Other races are subject to DM approval.
NOTE: Players should never feel constrained by the typecasting of non-Human species, but NPCs always act according to type. Only Humans have true diversity.
Dragonborn
Dwarf
Elf
Gnome
Halfling
Human
Once again, Player Characters should never feel forced to play to type, but NPCs will almost always conform to the types described.