An interesting discussion has been going on at Ta-Nehisi Coates' blog about whether Jews are white (Caucasian).
As an Ashkenazic Jew myself, I will offer my perspective after the jump, but I also wanted to poll Kossacks to find out the general perceptions here.
I've always identified as white, whenever people have asked. If someone wants to say, "No, you're not white, you're a Heeb, man," my reaction is going to be, "Okay, whatever."
But I've occasionally met fellow Ashkenazi Jews who do not consider themselves white. These people point out correctly that Jews were once considered nonwhite in the United States. Of course, the same was true for many European ethnicities, including Germans and Irish. (There's a book called How Jews Became White Folks, and another called How the Irish Became White.) This has far more to do with social status than with biology, but then that's always been the way race has worked in our society.
The thing is, as an Orthodox Jew, I find the question "Are Jews white?" rather silly. Jews, according to Judaism, are not a race nor a subset of a race. A Jew is traditionally defined as either one who has a Jewish mother, or a non-Jew who converts to Judaism. Thus, ancestry plays a strong role in Jewish identity, but it isn't the whole picture. Wikipedia describes Jews as an ethnoreligious group, a concept largely unknown in the West but not uncommon in other parts of the world.
There are in fact Jews of all races and colors. People of African and Asian descent have converted to Judaism, or have been adopted into Jewish families and raised as Jews. (I personally know several such individuals.) There are a few historical Jewish groups who are clearly nonwhite, most notably Beta Israel (Ethiopian), Bene Israel (Indian), and Kaifeng Jews (Chinese).
Still, those are exceptions. Most Jews in the world are divided into three broad groupings: Ashkenazi, Sephardi, and Mizrahi. Ashkenazim, those with a family history in Eastern and Central Europe, tend to be relatively lighter-complexioned on average than Sephardim and Mizrahim, and since they constitute the majority of Jews in the United States, they have dominated the popular American image of the Jew.
The term Mizrahi (literally "Oriental") is generally applied to Jews with a family history in the Middle East and North Africa. Sephardi is a confusing term. Strictly speaking, it is used to designate Jews with a family history in Spain or Portugal. In the late 1400s, Iberian Jews who refused to convert to Christianity were expelled from the peninsula and settled in various other countries throughout Europe, Asia, North Africa, and even the New World. Because they are so widespread, Sephardi has come to be used as a virtual synonym for "non-Ashkenazi." While this practice is not strictly accurate, it is pervasive in the media.
Some people perceive that Ashkenazim are white but Sephardim and Mizrahim are nonwhite. A while ago, the New York Times ran an article about the debate over Christopher Columbus's ethnic origins. When it came to the hypothesis that Columbus was Jewish or of Jewish descent, it made the following curious remark (this quote isn't in the online version of the article): "Most Jews in Southern Europe at the time were Sephardic Jews of North African descent, but preliminary analysis of Columbus's DNA suggests he was Caucasian."
This statement shows ignorance of the fact that genetic studies suggest a close kinship between Ashkenazi and Sephardi Jews. And I have no idea where the author of this article got the idea that European Sephardim were of "North African descent."
The racial status of Jews ties into the racial status of Arabs and other Middle Eastern groups. Are Arabs white? According to census forms, they are. But in popular imagination, they are often distinguished from whites. Of course many Arabs show evidence of having a mixed racial background. But the same is true of Jews from the same countries. Yemenite Jews often look black or nearly black. Paula Abdul is partly of Syrian Jewish ancestry (the other part is Ashkenazi) and many people have incorrectly identified her as black.
Many anti-Zionists have seized upon the largely discredited Khazar hypothesis, which supposes that most Ashkenazim are descended from European converts, and therefore are more ethnically European than Middle Eastern. There's no question that Jews mixed to some degree with the native populations of the countries in which they settled, and European Jews are no exception, but the evidence suggests that overall Jews are still fundamentally a Middle Eastern people.
Jews and Arabs are in fact closely related, and in Israel, where the Jewish population is about half non-Ashkenazi, it is often hard to tell the two groups apart. Race may be an imprecise scientific concept, but as long as we're going to invoke racial classifications, we might as well try to be a little consistent. And classifying Jews as white but Arabs as nonwhite is the height of absurdity.
In sum, I don't care what race you consider Jews to be, if any, as long as you're consistent and show at least some knowledge and understanding of the complex history and social dynamics of the Jewish people.