I'm not a geneticist, but from what I've read in this article, there are clearly biological / genetic differences among races.
I suspect race doesn't fall into discrete categories (like chairs couches and tables are different types of furniture) but along continuums (black to white, then adding an extra dimension for asian, etc.).
I have no idea how good this journal is, but here is a short but technical article arguing that races exist as biological constructs.
http://genomebiology.com/2002/3/7/comment/2007
Quick quote from the article:
If biological is defined as genetic then, as detailed above, a decade or more of population genetics research has documented genetic, and therefore biological, differentiation among the races. This conclusion was most recently reinforced by the analysis of Wilson et al. [2]. If biological is defined by susceptibility to, and natural history of, a chronic disease, then again numerous studies over past decades have documented biological differences among the races. In this context, it is difficult to imagine that such differences are not meaningful. Indeed, it is difficult to conceive of a definition of 'biological' that does not lead to racial differentiation, except perhaps one as extreme as speciation.
***
Despite the evidence for genetic differentiation among the five major races, as defined above, numerous studies have shown that local populations retain a great deal of genetic variation. Analysis of variance has led to estimates of 10% for the proportion of variance due to average differences between races, and 75% of the variance due to genetic variation within populations. Comparable estimates have been obtained for classical blood markers [15,16], microsatellites [17], and SNPs [12]. Unfortunately, these analysis of variance estimates have also led to misunderstandings or misinterpretations. Because of the large amount of variation observed within races versus between races, some commentators have denied genetic differentiation between the races; for example, "Genetic data ... show that any two individuals within a particular population are as different genetically as any two people selected from any two populations in the world." [18]. This assertion is both counter-intuitive and factually incorrect [12,13]. If it were true, it would be impossible to create discrete clusters of humans (that end up corresponding to the major races), for example as was done by Wilson et al. [2], with even as few as 20 randomly chosen genetic markers. Two Caucasians are more similar to each other genetically than a Caucasian and an Asian.
In these variance assessments, it is also important to consider the frequency of the allelic variants examined. These studies are based primarily on common alleles, and may not reflect the degree of differentiation between races for rare alleles. This is an important concern because alleles underlying disease susceptibility, especially deleterious diseases, may be less frequent than randomly selected alleles. Similarly, it has also been shown that among different classes of SNPs, those that lead to non-conservative amino-acid substitutions (which most frequently are associated with clinical outcomes) occur least often, and when they do occur they tend to have lower allele frequencies than non-coding or synonymous coding changes [12,19,20].
