Well, a quick count indicates 404 playable D&D humanoid races in my index. That is actually even more than the number statted up as creatures, thanks to the seemingly endless number of dwarven, elven, gnomish, etc. subraces that have appeared throughout D&D history.
And then there are a whole bunch more non-Humanoid creatures playable as characters (17 Aberrations, 4 Constructs, 16 Dragons, 6 Elementals, 21 Fey, 27 Giants, 8 Magical Beasts, 118 Monstrous Humanoids, 64 Outsiders, 5 Plants and 3 Undead).
So I estimate that there are just short of 700 creatures that are (theoretically at least) playable as characters.