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genetic grouping, on a par with Ashkenazim or Icelanders
Knowing that someone has substantial Ashkenazim ancestry lets you make many probabilistic predictions about both neutral and significant genetic variations (e.g. diseases, lactose tolerance, etc). This is because of the fact that historically mating behavior was highly nonrandom across geographical and ethnic lines. Since selection pressures and new mutations varied by region (see lactose tolerance, malaria resistance, fast-twitch muscle, salt retention, etc, etc) the differences predicted are enriched for differences due to natural selection, i.e. interesting ones that actually made life-or-death differences in the past.
Learning that someone is of European Ashkenazi descent lets us (probabilistically) predict a variety of genetic differences from the European average at each of many loci, and to very accurately predict, in the aggregate, a systematic skew across many loci to the Ashkenazim distribution.
"Race" is a magical category that does not carve the gene pool at its joints.
This is just factually wrong. You can use many, many different traits, or just neutral variation to easily cluster humans in a high-dimensional space of genetic variance. The oceans, the Sahara desert, the steppes, and other geographical features were major factors in historical reproductive isolation, and the largest (and quite clear) clusters correspond pretty well to the old anthropological classifications. If you tell me some facts about bone structure, body fat ratio, malaria resistance genes, whatever, I can quickly assign high probability to a given mix of recent continental ancestry for an individual and make much better predictions about other traits using that info than I could without using that clustering. In the U.S., self-identified race is itself a very strong predictor of continental ancestry, and if one supplements with further questions about grandparents' race or asks about multiracial ancestry it gets even better.
This post by physicist Steve Hsu discusses the topic well, also see this paper by Risch et al:
http://infoproc.blogspot.com/2007/01/metric-on-space-of-genomes-and.html