If you check out the Khazaria site you will get your fill on information on the ancient Khazar people. I don't really understand why so many modern Jews are fixated on the Khazars, as there is now a Jewish state (the medieval Jews took heart that a temporal power had chosen their religion over Islam and Christianity). For those not in the know, Khazars were a Turkic tribe of the lower Volga region who were a dominant power between the 7th and 10th centuries. Though the Khazars are most famous for the fact that their elite chose Judaism as their dominant religion, their most important role in history was probably their alliance with the Byzantines and the fact that they blocked the northward push of Arab Muslims (though I suspect that climate would have turned against Arab military tactics at some point as one went north in any case).

Much speculation has been aired about the Khazar contribution to Jewish genetics, but people often forget that it is a fact that the Khazar aristocracy intermarried with Byzantine Imperial lines. In any case, my personal introduction to Khazars was watching an evangelical Christian program on a Sunday morning in the 1980s. The basic thesis of the program was this:

• Ashkenazi Jews are descended from Khazars, Sephardic Jews are descended from ancient Jews.
  
• Ashkenazi Jews are more militaristic (Yitzak Shami was given as an exemplarr), while Sephardic Jews are more dovish (Shimone Peres exemplar).
  
• The world will come to an end because of the machinations of Ashkenazi Jews (armageddon).
  

Israeli readers will note that the "facts" offered during this program are at variance with reality on several points, and this has perhaps made me reflexively cautious about any talk of "Khazaria" (oh, and the fact that many anti-Semitic theories incorporate Khazaria, especially those influenced by Christian Identity).

Nevertheless, I was pointed to this paper in The European Journal of Human Genetics titled Y chromosome evidence for a founder effect in Ashkenazi Jews. Near the end, the abstract concludes "...R-M17 chromosomes in Ashkenazim may represent vestiges of the mysterious Khazars." I found this website which reviews the lead author's previous work (again, allusions to Khazars). The paper suggests that the marker in question entered the Ashkenazi community early on, which seems to make an argument for an incremental introgression from the surrounding Eastern European population less plausible. Nevertheless, I still think it seems more likely that, for example, Jewish merchants in Germany purchased Wendish (West Slav) slaves who adopted Judaism (the Wends were pagan, so German Christians could enslave them and treat them like animals without too much objection from the Church, and while it was illegal to convert Christians to Judaism, I have read that there was less supervision when it came to pagans, even if the said pagans were nominally baptized and Christianized), than that somehow the Eastern European marker wended its way into Jews via the Khazars (remember, the Khazars were by origin a Central Asiatic people).² I think the highest plausibility thesis of why the Khazars keep showing up in papers is that they are sexy (much more sexy than marginalized Slavs) and it guarantees publicity in the popular press.

Update: Here is the full paper (PDF).

Related: Multiple Origins of Ashkenazi Levites: Y Chromosome Evidence for Both Near Eastern and European Ancestries (again, a nod to the Khazars). A post where I collected links to many studies about Jewish genetics with summaries.

1 - Turkic shamanism, Christianity and Islam were also Khazar religions, though not as popular among the elite.

2 - Note, I am not asserting that Wendish males Judaized and so brought the marker in question into Ashkenazi Jews, I am simply offering that I do not find this any less plausible than the Khazar vector hypothesis, but you will not see this alternative offered because it is far less "sexy" a thesis.