Did the universe have a beginning? If so, need there have been a cause? Can time have been infinite in the past? Does physics have anything to say about these issues, or are they purely philosophical? Or meaningless?
Thanks to Peter Woit of Not Even Wrong, I came across these two blogs dealing with cosmology and its philosophical implications. Peter says the list of questions on the first blog are "orthogonal to ones I find interesting." If your interests are not completely parallel to Peter's, you might want to check them out.