Buddha tells us not to think too much about these questions - how did world come to be, manifestation of karma, if beings exist after death etc, because these do not lead to cessation of suffering. He said he only teaches cause of suffering and cessation of it. Nonetheless, we all think about rebirth, it is a concept that can not be easily ignored. I was raised a Hindu and hence, this concept has been a part of my life since I could remember. Now the thing that was puzzling me is that Buddhism also talks about continuation of conscience, which takes birth based upon its karmic load. I was really not able to differentiate between rebirth in Hinduism and Buddhism.
In the meanwhile, I have been meaning to go to Bhikku Bodhi's lecture in Chuang Yen monastery for a long time and finally was able to go. Coincidentally, this was the topic of the day. He said something which was an aha moment for me. He clarified that the difference between Hinduism and Buddhism wrt rebirth is, that Buddhism does not recognize concept of a non-changing, permanent soul or atman, that goes through cycles of rebirth and hence attachment to this self. There is a stream of consciousness, which changes forms, like wood changes to smoke, when burnt, but no permanent entity. Hinduism considers soul as permanent and hence, also strengthens the notion of self. Soul or not, permanent or not, for me the key was attachment. If you believe in a non-changing self, there lies the attachment, which gives rise to Dukkha.