Dear Twisted:
Virtually every Jew is probably descended from the Khazars. We know that while most of the Jews in Khazaria came from the Byzantine (Roman Empire, then centered in Turkey and Balkans), when it split up most of them probably went to Babel (Iraq) and Spain, but some ended up in other places in Europe. Of the course of 50 generations, given that we have a small population, everyone is a cousin to everyone else. It is highly likely that unless you are a recent convert, you are related to every Jew alive in the 9th century.
Linguistic and DNA evidence though, suggests, that the Khazar contribution to the Jewish gene pool was very slight. Jews are quite dissimilar from the Central Asian Turkish tribes, and languages such as Yiddish have very words of Turkish origin. The reason much fuss is made of the Khazars as some frei Jews desperately wanted to be of non-Jewish descent so they could: 1) tell the Czar they shouldn’t be persecuted for killing his diety; 2) tell Hitler they were really Aryans; 3) find a secular excuse for not supporting zionism