I would have to do some digging, and may decide to later, but when I was seriously considering Judaism as the possible true religion, I frequently read hasidic documents and stories, and there most certainly IS a belief in reincarnation, at least among many Jews. However, it is not a belief that everyone is reincarnated, IIRC, but rather that some people had died before completing some task or mission they needed to, and so come back attached to a new body (it's been a while since I've read about this, but as I recall there were two main lines of thinking in the stories and documents I read, those being that the souls of such people were attached to new bodies that had their own souls, sort of like two people in one, and the other line of thinking being that it is a completely new body for the person). One such story I recall reading is of a Rebbe who had incredible spiritual insight, and there was a woman who came to him because she was pregnant for a while past her due date (I believe nearly a week), and was getting worried. Earlier, he had seen an old man who was on the verge of death, but not quite there. Anyways, I don't recall specifics, but he determined that the woman would give birth only after the man dies, and I believe he even saw the man's spirit go into the woman right before she went into labor.
Anyways, my point is is that - at least among those Jews who would care about Kabballah (the actual Jewish thing, not the pop-religion thing) - a belief in reincarnation actually does exist.
EDIT: I would also note a belief that the Messiah is present in every generation, just waiting for the right circumstances to fall into place before revealing himself. As such, depending on exactly how this is understood, this could also be a case of reincarnation.