On 26 November 2010, Icelandic psychologist Prof. Erlendur Haraldsson was the keynote speaker at a symposium on reincarnation research in Leiden University. He presented some recent cases he studied and discussed the theory choices suggested by his findings.
Testimonies suggestive of reincarnation are mainly of two types: children below 7 spontaneously claiming past life memories, and adults taken back to earlier stages of their lives (and pre-lives) in a semi-hypnotic state. Haraldsson's research focused on the children's testimonies. Sometimes these are startlingly accurate in describing someone's life and, once the deceased person is identified and the child taken to his life setting, in recognizing places and people.
There are five possible explanations. Two of these are non-paranormal: coincidence and fraud. Three are paranormal: possession by the ghost of the deceased, telepathic retrocognition, and reincarnation.
Since there exist cases where a child recollects the life of someone who died after the child was born, and some where multiple children recollected a single person's life, I am inclined to vote against the reincarnation hypothesis. A transmission of memories either through telepathy or through ghost possession, though to a lesser degree still paranormal, seem more plausible and fit the data better. More likely, those testimonies are similar to what Jim Morrison described in An American Prayer in a recollection of a childhood event where he witnessed a truckload of Amerindian workers dying in a traffic accident: "The souls or the ghosts of these Indians had entered my head... and stayed there." Or in the musical version, Peace Frog: "Ghosts crowd the young child's fragile eggshell mind."
As the child grows up, its mind develops better defences and chases the ghost along with the recollections out. That should explain why by age 10, those children have generally forgotten their "past-life" memories. But we can safely conclude on the worn-out yet highly apt remark: in this promising field, more research is urgently called for.