As a multiracial person, this isn't a question that I've considered much until adulthood -- throughout my childhood in the American South, I had to keep a safe emotional distance from people, and my parents didn't let us consider it. Now that I'm older, I'm able to link some aspects of my experiences to the fact that I am a mixed-race person, and people have difficulty perceiving and placing me...
For instance, I recently had a professional engagement, and after speaking to a woman at some length (she happened to be of European descent), she suddenly asked me what languages I speak, and so I answered honestly.
I now realize that this is a way people have of trying to place me, socially, ethnically, and racially in a way that isn't abrasive or alienating. It gives people social cover... My students tend to ask me very strange questions when they first encounter me, particularly what kind of music I listen to and where I was born -- sometimes, one student will just spit it out, "What are you? Where are you from?"
I've noticed that peoples' reactions or a strange mix (pardon the pun) of curiosity, alienation, enthusiasm, fetishizing, and even erotic attraction -- I find it bewildering but interesting. What further complicates peoples' perception is that I am, truly, multiracial: racially ambiguous along the white/black lines, but also part Asian (I self-identify as a multiracial Black woman, or a Creole).
So how do you feel about multiracial people?