First of all, I have never heard of any evidence or reasoning for reincarnation. Second, I think that it sounds too much like a cheap paperback novel. Third, everyone is born with a sinful nature anyway and the only way to be cleansed of that is through Jesus.
Yes I do believe in reincarnation. I am now a Hindu, but I believed in reincarnation even before I was a Hindu. To me it is in line with a compassionate God who created us with a purpose. If we do not fulfill our purpose the first time, or we royally mess up, why would he not give us another chance?
Besides that, it also seems to be the best explanation for various stories I have heard from what I believe to be reliable sources.
When I was a King in a past life I had my Wise men research this question and they said, "No, it is not real" Maybe they were correct. BUT, in a round about way it can be true from a Bible point of view. Christians will die and their Body turn to dust in the Ground or through Cremation. THEN, the Bible says WE will be given a NEW body. So, Theoretically, Christians will be Reincarnated into a New Body, but, that just a Word Play I use.
I am not a Hindu. I was raised a Christian Spiritualist. I was raised to believe in reincarnation; but I don't actually KNOW one way or the other. Also, like the question of the existence/nature of God; its not relevant to the practice of a decent life.