Diverse races are not that important for a play character as the race doesn't make a difference to who the character is, and considering the amount of publicity anything race-related has in games, simply have the character be the standard white male makes it a lot easier than accidentally slipping into the racism pool, while trying to fit the mannerisms to the race (no, its not racist to understand that while race does not define a person, it does affect them and ignoring this would simply create the standard male character just with different coloured skin)
So yeah, for the most part Race is left out of the protagonist it isnt however abandonned with the supporting characters, and this is where the development and progression is. As better and better divrsity creeps into the support character role it breaks down from the stereotypes formed and develops better characters, from this developpers may become confident enough to create decent player characters whose race is not the standard white males, and it make no difference to the storyline but still be believable.
Although i would also like to point out that a lot of games take place in white dominated countries. So a realistic (because we all like realism) probability is that the protagonists would be white.
A lot of RPGs (such as ME as mentioned) Allow you to play as a customizable character.
Some games give you a selection of players to play as, such as the L4D series, both games have a black characters, and i would probably expect different races it shows how the design of a game limits the portrayal of race, l4d has 4 open slots, and the game must therefore create 4 characters with personalities... you can't fit the entire spectrum of races in 4 character slots. Almost every other game only has one protagonist, imagine how hard it would be to do that?
So okay.
Games where you can play as another race:
GTA:SA
GTA:4
Mass Effect (custom)
Fallout 3 (custom)
The Elder Scroll Series. (custom)
Call of Duty MW
L4D1/2
Saints Row (custom)
Dead Island
Prince of Persia
Games with different Raced support Characters:
Half Life 2
Crysis
Resident Evil 5 (no, the game isn't racist just because the bad guys are a different color this time, thats what happens when you go to a different country.)
Final Fantasy
And game set outside of the white dominated parts of the world.