Considering that, in America, the most popular games are NFL and NBA games, I would say that non-white characters make up a very good portion of playable characters in games.

Non-black characters are in the great minority here.
Yes, I am being a bit satirical here. I would guess that, historically, the majority of characters are Asian or white. In the worlds the designers live in, this is what they experience; Japanese living in a society where almost 100% of people are Asian. When they come in contact with non-Asians, it is usually through American TV where Caucasian people are of the majority. On the Japanese side of things, this is just a product of environment. Likewise with western-produced games, most of the designers grew up in a mostly white environment (I am guessing here, but I think it is a good guess). The games they create are a product of this.
I imagine that most games I play feature Asian characters, since I usually play Japanese-produced games.
Anyway, I'm done. I'm going to play some GTA: San Andreas.

Something tells me there are a few stereotypes going on here...