In phylogenetic systematics one of the necessary preconditions for the recognition of a taxon is its monophyletic status. In other words, members of a taxon must share common descent, and not just relative similarity as in phenetics.
If three groups of organisms A, B, C are such that A and B are more similar to each other than they are to C, then phenetics would consider classifying A and B in one taxon and C in another. By contrast, phylogenetics would try to establish whether A and B share common characters derived from an ancestor that was not an ancestor of C. If it turns out e.g., that B and C have such an ancestor, then B and C should be grouped together, even though B is closer to A than to C.
It has long been established that human beings can be grouped into clusters corresponding to major "continental" populations. This has been achieved using cranial traits, classical polymorphisms, as well as more recently large numbers of microsatellites. Therefore, we are justified in thinking about the existence of human races in the phenetic sense.
However, recent advances in phylogeography, especially based on uniparentally transmitted markers on the Y chromosome and mtDNA have shown that human continental populations which correspond to phenetic races such as "Caucasoids", "Negroids", "Mongoloids", etc. do not correspond to monophyletic groups.
For example, almost 9 out of 10 Ainu trace their paternal lineage to an ancestor who has also fathered approximately 9 out of 10 Moroccans and South African Bantu. That man, who first carried the YAP mutation, lived either in Asia or Africa, and yet his descendants belong to three of the major human races.
Similarly, 9 out of 10 Basques are descended from a man who has also fathered 9 out of 10 Kets from Siberia and 9 out of 10 Maya Indians from America. That man, founder of haplogroup P thus has descendants who belong to two of the major human races (or three, if Amerindians are considered as separate from Asian Mongoloids).
Thus, despite the close proximity between, e.g., Spain and Morocco, and the genetic and phenotypic similarity of their inhabitants, who are considered to belong to the Caucasoid race, it is the case that phylogenetically, Spanish Basques and Mayan Indians share recent ancestry not shared by Moroccan Berbers, and conversely, Moroccan Berbers share recent ancestry with South African Bantu not shared by Basques.
Should we then acknowledge the existence of a "YAP race", or a "P race" on the basis of these observations? Not at all, since by examining other phylogenetically informative systems, e.g., mtDNA, it turns out that Basques and Moroccans are phylogenetically linked to the woman founder of mtDNA haplogroup N, while Ainu and Mayans are linked to a woman founder of mtDNA haplogroup M.
In conclusion, human continental populations form groups of genetic and phenotypic similarity, and these groups can be considered races in the phenetic sense. However, these groups are not monophyletic, hence in the cladistic sense they should not be considered as valid taxa. Since the principle of common descent is generally applied in modern systematics (or at least it should!), I think it's best not to recognize human subspecies.
We may still however speak of human races as clusters of biological similarity, or as ecotypes, if we keep in mind the understanding that the commonly recognized races are not phylogenetically justified.