There are some strange stories that one keeps hearing. Like a young kid in a village start speaking American accented English suddenly without any education and this being attributed to reincarnation. I guess this incident was reported in a UP village a few months back. I guess most of such things are made up and die their natural death.
Hindu religion does believe in reincarnation. I think the idea is that you are struck with the cycle of life and death till you manage to get out of it by pleasing God.