If you read enough "past life memories," including both hypnotically recovered and spontaneous ones, a few things become clear.
1) These memories are not genetic in the usual sense. When children spontaneously remember recent, traceable past lives, they may or may not be related to their original, but the relationship is seldom direct if it exists at all. In order to account for reincarnation genetically and still treat it as a single phenomenon, you'd have to find a way to trace genetic links laterally across generations; at which point you've left the realm of falsifiability far behind, because if you try hard enough you can link us all back to mitochondrial Eve. (BTW, male lines can also be traced back to a single Adam figure, who never met Eve; the process is described exhaustively in *The Real Eve,* Oppenheim).
2) Memories that can be traced to a documented supposed past life usually contain startling accuracies - but they also contain puzzling inaccuracies which reincarnation enthusiasts overlook with an enthusiasast's normal insouciance.
3) Past life regressions which can be demonstrated to be false nevertheless relieve symptoms.
4) Past life memories recovered under hypnosis correspond to the expectations of the hypnotist most, but not 100%, of the time.
5) Spontaneous past-life memories in young children are more interesting and more puzzling than the ones generated by hypnosis.
What does it mean? What does anything mean?
Readily available books to see for yourself:
Children's Past Lives : How Past Life Memories Affect Your Child
by Carol Bowman
OLD SOULS : Compelling Evidence from Children Who Remember Past Lives
by Thomas Shroder (Author)
Alas, though I conscientiously write down the titles and authors of books I read in the back of my diary, I cannot identify the book by the man who started out to prove that his memories of a life as a painter were entirely confabulated, but turned up startling evidence that they weren't - except that he was completely off on the name of the obscure original's wife. I'll have to hunt this up again, as it was a new book when I read it and it was fabulously Fortean, with the author chasing down an endless hall of mirrors finding answers that led only to more and more questions.