Memories of Recycled Souls?

He had enjoyed his present life but his principal regret to leave it would be that he must pass through that strange barrier which blots out all but the vaguest intuitive memories of earlier experiences before a soul is born again. (Dennis Wheatley, They Found Atlantis)

     It is hard to know how many people in the Western world believe in reincarnation. One survey said 24% of Americans, but even that statistic is meaningless unless you inquire about the strength of the belief. For every person who is certain of reincarnation, there will be many more who consider it probable or merely possible. Rather like belief in God or flying saucers, in fact. As far as I can ascertain, such beliefs were not common in the west prior to contact with eastern religions. But the believers are not, by and large, Buddhists or Hindus; experience with other cultures has merely raised a possibility not previously considered. If you ask them for a reason, you may not get a very coherent reply. A friend of mine said that reincarnation made the universe "fairer", as if there were some unwritten law that the universe must be fair. So, what exactly is the evidence for reincarnation?