The Science of Reincarnation | The University of Virginia Magazine
The work of the late University of Virginia Professor Ian Stevenson on reincarnation was mentioned in comments here recently, and I see now that the University still has a psychiatrist who conducts research on the topic.
The link gives a pretty good example of one case he knows about in detail.
I am a bit surprised to see that 70% of children who suddenly claim to have lived before are male. But it is interesting to hear of American cases. If I recall correctly, one of the big issues with Stevenson's work which (I think) dealt with a lot of Indian cases, is that the kids were being raised in a society which already accepts reincarnation, and they would surely be influenced by that in their imaginative life.
That's a lot harder to see as an influence in America.
You should also read the comments following the article. Some people are "appalled" that the University magazine would run such an article.