I've heard Rudolf Nureyev, Vaslav Nijinsky, Irek Mukhamedov, Farukh Ruzimatov, and Altynai Asylmuratova all described as "Tartars." Excuse me if I sound really ignorant but what exactly does "Tartar" mean? Is it an ethnic group? AFAIK the above-mentioned dancers all came from different places geographically (Asylmuratova is from Kazakhstan, Nureyev from Ufa). Or is it sort of a general description of a kind of appearance?

Tartary was a humongous piece of territory that extended from the Sea of Japan all the way to the Dneiper River and included northern China, all of Mongolia, most of southern Russia and was inhabited by groups of Tatars, an ethnic group. Tatars are mostly from the Turkic language group.

Tatarstan was (is?) an autonomous republic in the old Soviet Union.

After the breakup of the USSR, when all of the republics rushed their own currencies into circulation, Tatarstan (reportedly!) had the distinction of issuing currency with no denomination (value) on it.

The following pages about Tatars or Tartars (both spelling exist- but it seems that Tartar can sound a bit archaic or offensive) might be useful:

http://en.wikipedia.org/wiki/Tatars
http://www.ainurin.net/history/tatarstan.htm
http://tatar.yuldash.com/189.html

Nureyev was born in a train near Irkutsk in Siberia and was raised in Ufa, but I've read that his father was of Tatar descent. I don't know about the other dancers your mentioned... (as far as I know, Nijinsky's parents were from Poland, but there are Polish tatars too).