I like what Morgan Freeman had to say. (h/t to JDZ )
It has long been accepted in my field of anthropology* that race is not biological, but is a social contruct. Categories of any kind, including categories of people, do not exist in the natural world. They are created by culture. In the natural universe, every object is in some ways similar to and in other ways different from every other object. Categorization defines certain similarities as important. This is not necessarily a bad thing! In general, categories are useful, which is why we create them. I can, for example, easily say something about waterfowl, or staple crops, or registered voters. Without categories, I would have to name each individual that I am speaking about, which would be hugely impractical.
The category of race, however, is one that I think is harmful rather than helpful, at least in the United States in 2011. I believe it would be a good thing if we would stop thinking of people in racial terms at all.
*In the U.S., archaeology is taught as a sub-field of anthropology.