As I look back over the long history of the Jesus quest (and its popularized sidekick, Jesus in cinema), I continued to be struck (and I admit ashamed) that Jesus rarely appears as a Jew. There have been occasional voices over the last century that have demanded we remember that Jesus was Jewish, but these have been occasional and against the communal representations of Jesus that were developing in those eras.
And sadly this includes the Third Quest which largely has been trying to get around the fact that Jesus was Jewish by creating categories for Jesus as a Hellenized person living in Palestine or Galilee, but a person that doesn't look like any other Jew we know of who lived in Palestine or Galilee. As Rebecca Lesses noted in her comment, the Cynic Jesus is "bizarre." And it is our methods that have allowed us to feel "good" about our bizarre reconstructions, particularly the dissimilarity principle, which is nothing more than a way for us to create a "unique" and non-Jewish Jesus that will sit better in the Christian cradle.
Now there are a whole lot of reasons why scholars - particularly Jewish scholars and Christian scholars - don't want to talk about Jesus as a Jew. Since my own heritage is Christian, I can speak to that most directly. To be frank, the Jewish Jesus is completely irrevelant to Christianity today. He does not make sense, because all that he stood for that was Jewish, he no longer stands for in Christianity. What would Christians do if they really took seriously that Jesus was kosher, that he demanded his followers observe the Jewish Law in a way quite similar to Rabbi Hillel, that he believed his mission was to Israel, that his holidays were Jewish, that is Sabbath was Jewish, and that the eschatological Kingdom he was talking about never came?
It has only been in the last eight or ten years, as far as I can tell, that scholars as a collective voice have been reacting to this problem in their publications on the historical Jesus, demanding that we take seriously the obvious - that Jesus was Jewish. Jesus as a Jew is not just another agenda-driven "construct" as some have been suggesting (this really is a hyper-post-Modern stance). Being Jewish was Jesus' self-identity, and it has taken us two thousand years to admit it and talk about what it means. No amount of pressing the button on the "diversity" and/or Hellenization of early Judaism is going to erase the fact that for Jesus the Torah and prophets were his scriptures, the Temple his cult, Yahweh his god, and the coming of God's Kingdom his hope. Jesus as Jewish is probably the most essential (and dangerous) idea that I can think of.
Update 4-14-07: some interesting responses on other people's blogs