Every time I read the title of this thread I think..."REALLY? Is this a real question?"
I don't even know what kind of answer to give.
I understand rainshower's point. I am mixed but I don't think it's obvious to most people, white OR black. Taken at face value, I realize most people see me as "just" black--they don't see or know that this is literally half of the equation. So while I have heavy influence of both sides/halves of my background to shape my mind/personality, I also have a knowledge of how I am perceived by most other people based on appearance alone. If I had to pick one of the other, I would say I'm black because that is I am viewed by most of society (and race is pretty much a label made by society). If I came out and claimed to be white, even if I am just as much white* as black, I know people of all races would look at me as if I had three heads. Do I look white? No. Do I look black? Yes. Is it really that simple? Of course not!
Did that make any sense? Probably not.
*(okay, Italian, which is another ethnic-race debate all on its own)