This is going to be a page of links about Reincarnation stories which appear to have some evidence behind them. I will add links as I find them.
The stories I find most interesting are the ones in which a person not only has a memory of a previous life but also looks like the person they say they remember. It is going to be interesting to see if the children who remember past lives actually look like the person they say that they were.
Reincarnation from World War II
There is an American boy called James, who believes he was a pilot in the second world war, shot down by the Japanese.
Martin Heald memories of Richard Seymour. Part One. Part Two.
Reincarnation from 20th century
Child remembers previous life, other family.
Reincarnation from previous centuries
Four cases from Australia, where the hypnotist takes the women to see the places where they say they lived.
Reincarnation of Paul Gauguin and his wife Mette.
Reincarnation from US Civil War
Jeffrey Keene, a retired firefighter, who believes that he is the reincarnation of General Gordon.
Ian Stevenson's work
Video about reactions to Ian Stevenson's work.
Michael Newton's work
Michael Newton is a hypnotherapist who has come to specialise in past-life regression. His website is here.
Work of Joseph R. Myers
Joseph Myers' page of photographs and possible links was the first place that I came across the idea that a reincarnated person might look like the person they claimed to have been in a previous life. Some of these cases, particularly those involving a husband and wife, are pretty convincing.