Actually in Judaism we're much more concerned about your mother. According to traditional Jewish law we are a matrilineal religion, meaning that Judaism is passed through the mother. The Reform movement accepts children who are the product of intermarriage regardless of which parent is Jewish.
Judaism is matrilineal because you can always tell who the mother of a child is. The roommate would argue that Judaism is matrilineal because we are a patriarchal culture that doesn't trust women to know who the father is. I'd disagree. I think that in biblical times territorial wars were pretty frequent, and rape was a common product of war. In those circumstances would you want to traumatize the mother farther by suggesting that her child isn't Jewish? Or, just practically, if the kid isn't Jewish you get into all sorts of issues that would be better avoided.
The results of matrilineal descent are a little bit different in the modern era. We in the western world often keep our father's last name (to the exclusion of our mother's), so you might be technically Jewish, but have no way of knowing. Just like Christine Axsmith who just discovered her Jewish roots. Or, more famously, Senator Macaca himself, George Allen. In the wake of the holocaust it is more common than not that a "good Christian" will find out that their parents were hidden children who were either forcibly converted as children, or grew up with Christianity as the only religion that they knew. One of the best examples of this is Cardinal Lustiger, he was a hidden child, and grew to believe in Catholicism so devoutly that he became a priest. When Pope John Paul was ill, Lustiger was one of the candidates to become the new pope.
Now I don't have an issue with this, I think that you should only be Jewish if you want to be, no one should be Jewish against their will. It is a hard row to hoe, even in these comparatively tolerant times. I do, however, have an issue with the thinking that Dr. Jim West mocks in his post about Christine Axsmith. Christine and others assume that there are particular characteristics that define Jewish people. In this case an interest in biblical archaeology, and a "curious affinity" with Jews. I'd just like to state that while I feel strongly that there is a Jewish people, that I don't really feel an "affinity" with most of the Jews from my generation. Nor am I particularly interested in biblical archaeology. Harley is a better Jew than I. She admits to feeling a curious affinity for Jews, and when asked if she has an interest in biblical archaeology, she responded: you know I do.
Crap, guess I'm the only one.