During 20 some years in the New Age and even having conducted many past life regressions, I have, disappointingly, never once come across a case where evidence was given that was truly verifiable, or something that couldn't be known through normal means, although many people claimed their experiences "seemed so real." My own son talked of when he was a "doctor" in Mexico "when he was big," at age 2. He claimed my other son lived in China and was a "girl." Odd and seemingly out of the blue at the time, but not verifiable.
There is a big difference between the Western take on reincarnation and the Eastern, which involves transmigration of the soul into the form of animals, etc. In the West, the belief is that spirits have more than one chance at life on earth (as a human), the idea being that we are suppsed to be evolving into better more positive. loving humans who will no longer have to reincarnate once that goal is reached, and that in the meantime souls reside on the "other side," or in a spirit realm, so all souls are not on earth at any given time.
There doesn't seem to be much by way of solid, verifiable evidence for the existence of past lives, but the one exception, I thought, was Dr. Stevenson's book, which I read many years ago. At first glance it does seem impressive - one thing I found intriguing was the issue of birth marks that closely correspond with the person's manner of death. But a few months back I read Mary Roach's book "Spook," not exactly a scholarly tome but well written and thoughtful - she did a nice job with it, and in it she tells of going to India to work with a Dr. Rawat who worked with Stevenson in the 70s. She followed along on a typical investigation of a claim made by a certain family, and what she discovered was interesting. First, that most of the stories, by the time they reach the researchers, have been told numerous times to family and friends, possibly encouraging the children's stories to become more and more elaborate, as well as making it almost impossible to know what the original claims might have been. Second, there is a great willingness among these people to believe these stories and in general it is greeted enthusiastically and expectantly, giving the families an "excuse" to come together and party and share resources, etc. She said day to day life in these typically impoverished areas tends to be one of monotony, and her impression what that the child's supposed recognition of lost relatives had been exaggerated by the enthusiastic families who for a time have a claim to "neighborhood fame," something welcomed by whole neighborhoods. So there IS plenty of reason for the families to elaborate the claims, and the for the children to pretend or even play along. This is not to say that is always the case, but it does cast the phenomena in a slightly different light for me.

Just a few thoughts.
Having posted here for awhile I'm sure my ability to think critically and skeptically is still in the earlier stages, although I've made great strides and appreciate the members of this forum for bearing with me.
I have not read the books by Richard R - I'm curious if his findings were similar.