In traditional anthropological studies there are actually 5 races:These are:
1) Mongoloid (Asian and American Indian)
2) Caucasoid (European)
3) Australoid (Australian and oceanic)
4) Negroid (east African black)
5) Capoid (south African black)
The remaining peoples are mixtures or "mongrels" of the different races above.
This theory was originally proposed by Ashley Montague and has been disputed for years, but has still withstood the test of time to a large extent.
The biggest problem with this theory is that all races share 99.99+% of the same genetic materials which means that further division of race is largely subjective, and that the original 5 races were also probably just subjective descriptions as well. The above theory has been used by people in the past to support racism as well as to refute it.
All in all the preponderance of evidence suggests that race is for now a subjective term. Furthermore, until DNA technology becomes even better, then there can be no better answer than Dr. Montague's, but that in time we will probably find more detailed versions. Apparently none of the other people answering this question have ever been to college much less have degrees in anthropology.