Gene Expression discusses race and appearance, pointing to people disagreeing about whether Tiger Woods looks "Black" or "Asian." Not only is there a good discussion of the involved genetic dynamics, but the larger question of "why do we still focus on race?" is touched on.
Being of mixed descent myself, my appearance and behavior has confounded many people who have tried to "pin me down" as a certain race or ethnicity, much to my amusement (some have been wildly off) - I grew up always being asked the question, "So what are you?" And I wonder now, does it serve any purpose beyond satisfying curiosity to try to ascertain a person's race when so many other factors, like culture and nationality, contribute to a person's identity and perspective when interacting in the world? Many have speculated on the future of race, that we will lose the need for such distinctions because more people will claim mixed heritage (as shown by the 2000 U.S. Census) and will grow up with a cosmopolitan appreciation of all cultures, making attempts to reify race and ethnicity superfluous and inaccurate.
Speaking as someone who eats everything from sushi, kimchee and curry to gyros, crawdad boil, and stroganoff, I have to agree.
Addendum: Beyond aesthetic considerations, attempts to classify race and ethnicity can have very real economic impacts.