In Mass Effect I built myself a badass black Renegade and called him Marcellus. I also played as a white female Paragon. I made her hot at first, tried to go for Angelina Jolie 10 years ago, but she kinda looked ridiculous as the saviour of the universe, so I went for the Captain Janeway look.
Considered an Asian character, but the Asian eye options in ME are really ugly.
I'm a white male myself like - quite unsurprisingly - the majority here
In third person games I never get "ooh, that's me"-feeling anyway. The same goes for games with cinematic cutscenes, since I don't usually have out-of-body experiences when talking to people. That's why I love Half Life and other games that have cutscenes happen around you, while leaving you in character. Didn't have problems impersonating a white Asian chick in Mirror's Edge though.