Some have argued recently that there's no such thing as race. Anthony Appiah's In My Father's House and Color Conscious are probably the two most notable discussions. Scientists often take this view without realizing all the philosophical leaps in reasoning they've made to get to the view (see, for example, this article, registration required). Others think it's merely a social category (most philosophers who write on the topic, usually on the same basis as the scientists above but with more sensitivity to issues about human language and social catgegorizations. There are also two possible positions according to which it's a genuine biological category, one of which I think is easily refuted by the data. The other seems to me to be a legitimate view that hasn't been discussed by philosophers or scientists to my knowledge (though I think economist Thomas Sowell may have suggested such a view -- I'm not quite sure yet). Below are the arguments for developing and sorting out these various views.
Before you read this it might be helpful to look at my first two posts in this (sort of) series. First is a set of cases to test your intuitions on racial classification, with the followup giving the data from my students' answers to those same questions.