For those of us who straddle the Buddhist-Christian worlds, the whole business of reincarnation (a Hindu concept), rebirth (a Buddhist concept) and having a Soul (a Christian concept) can be problematic. Hindu spirituality poses the idea of reincarnation, a concept that has been accepted by more than a few Christians throughout history. Loosely stated, reincarnation holds that we come back and live again until we achieve enlightenment. In Christian terms we might say that we come back until we achieve union with the Divine, or union with all that is. In the New Testament there are references such as our being "purified as if by fire" that Roman Catholics have seen as a proof text for purgatory while reincarnationists (myself included) would argue that if this life is anything it is a purification as if by fire and so this must point to reincarnation.
Rebirth, on the other hand, holds that our essence returns but nothing more. For me the problem in that belief is that in Tibetan Buddhism great Lamas are not only reborn but are in fact reincarnated. In fact, the great masters are thought to be able to predict and/or control the place of their next "rebirth." When the suspected reincarnation is found, he recognizes the things that belonged to him and pictures of people associated with him in his previous life. Apparently, in the transition from schmuck to enlightened person to Bodhisattva the circumstances of rebirth/reincarnation change and come under the control of the individual - or something like that. Frankly, I'm not buying it. I am suspicious of all double standards, and to me (you can, of course, make up your own mind) the whole notion of Bodhisattva vow - that we vow to return even after achieving enlightenment until all beings are enlightened - rather argues against rebirth and in favor of reincarnation. Taking the Bodhisattva vow means that me, myself, and I - empty though we may be - are coming back.
Speaking only for myself, of course, I do believe I have a soul and I believe that soul is impermanent in that it is always changing/evolving because nothing in life stagnates without dying. I believe that soul carries over from lifetime to lifetime, and while I am ambivalent about the assertions of some that they can recall entire previous lives, there is the little matter of a recurring dream I had as a child of being dressed in fur and a metal helmet with horns on it, running through a town, and being run through with some kind of spear. I had this dream long before I knew what a Viking was, and long before I knew I was Norwegian. Then again, it may not mean anything.
Theologians constantly argue about things like this and make pious declarations of what we ought to believe - a grand display of arrogance if ever there was one. The truth is that nobody knows what happens after we die, and there is no proof that anyone has ever come back or even been reincarnated - though for my part I find the Tibetan system compelling. There is the little matter of the several "books of the dead" from antiquity that purport to tell us precisely what happens according to different traditions - but all they really are is collection of the speculations of ancient theologians, who seem no less arrogant that contemporary theologians. One might say they were ahead of their time!
In the end, I believe that what really matters is that each of us arrives at a resting place (as opposed to a conclusion) in our journey that we can live with. If it fits right now, I believe that is a good and beautiful thing - as long as we keep our minds open to new information and possibilities. Once we close ourselves to the possibilities, we close ourselves to growth and turn instead to paying more attention to defending our entrenched beliefs than to the beliefs themselves. There's a name for that, but I suppose I use it too often...just turn down the lights, light some candles, maybe play some soft music, because all productivity has ceased.