There is only one race classified as Homosapien sapien. However, the term race, sub-race would actually be correct, is also used to classify different groups sharing similar or the same physical attributes and genetic inheritance. Under that usage, there are definitely more than 3.
Amongst people with Black/dark brown skin pigmentation there are Sub-Saharan Africans, and even there there are different characteristics between geographical locations, there are the Australian Aboriginal Tribes, Tribes from differing south pacific islands and even jungle peoples of the Amazon.
I don't think there are very many who actually know just how many sub-races of the human race exist. I know I don't.