I've been somewhat interested in this idea ever since I heard about the investigative works of the late Ian Stevenson (2007), a psychiatrist and Director of the Division of Perceptual Studies at the University of Virginia School of Medicine. He is mentioned in the video below by the author Carol Bowman, who collaborated with him in studying the cases of children who claimed to have memories of past lives that were effecting them in the here and now. This includes roughly 800 documented cases by Stevenson. In this video (at a conference in Spain, hence the introduction in Spanish), Bowman speaks about her son, then five years old at the time in 1988, when he began professing to have been a black soldier wounded in a war by a gunshot to the wrist. He showed a clear phobia for explosions and fireworks before his revelations, and under hypnosis explained the reason why. He claimed that in his previous life, after his wounded wrist was bandaged in a field hospital while he rested on a bench-like bed, he was sent back to the battlefield to mind the artillery pieces drawn by horses and was ultimately blown up by enemy cannon fire. He drew pictures of the medical camp where he was treated, which somewhat resembles the American Civil War field hospital.
It's pretty striking to hear this testimony and see the drawings of this sort of thing from a five-year-old, but judging by the case studies of Ian Stevenson, is not exceptional. I was also rather taken aback by the child's claim that he was above the battlefield after being blown up, and was glad to leave the carnage and the death. I also found it interesting that he claimed that, as a spirit who had left the body, he was able to travel around space and time quickly.
By the end of the video she cites the case of James Leininger, born 1998, but as a young child claimed to be an American fighter pilot in WWII also named James, and flew his (Vought F4U) Corsair from the USS Natoma Bay aircraft carrier. When his father pressed him about any friends he had, the child said "Jack Larson." When researching the names of the people on the Natoma, they indeed found a Jack Larson. Like Bowman's kid, James also made drawings of his alleged past life, including planes being shot down. It appears there was a 21-year-old pilot named James Houston who was also on the Natoma and was shot down in 1945. As the video shows, little James Leininger had a "reunion" with the elderly Jack Larson, along with his alleged sister from a past life, Ann Houston. Upon invitation by a Japanese film company, Leininger also visited the place in Japan near Iwo Jima where James Houston was shot down and threw a bouquet of flowers there at the memorial site, saying he would "never forget you" (i.e. his alleged former self, James Houston).