PHB races will be accepted without question.
MM PC-playable races need to be signed off on by the DM, but will probably be accepted.
Any non-core rulebook race: Subject to DM approval. Player will be responsible for ensuring the DM has complete access to whatever source material the race comes from. Exempli gratia: If a player wanted to play a race from the MMIII, he would have to make sure the DM has a hard or soft copy of the MMIII.
Races with level adjustments can be accepted (within reason), but will have the appropriate level penalty.
Basically, if you want something, ask. The worst that can happen is you get told: “Eh, that’s a little too broken…”