I do. Naturally my entire belief structure is a little complex to explain here, but I shall try to summarize. I have had enough experiences in my own life that point me to believe I have lived before. I feel this is a continuing cycle in which we learn and grow in each life we live.
I do not believe we live one life and that is our shot to make it to heaven. I believe we are all part of our own grand social experiment in which we are all choosing to learn from ourselves in many situations. We may never know all the details of life after we die, but is that not part of the point? If we knew everything, we would not experience as deeply, would we?
Maybe time will tell. Maybe the point is that it wont.