Dr. Stevenson takes the classical scientific approach to the study of reincarnation. He is his own hardest critic, and in his scientific rigor, dimisses any case which has any reasonable explanation other than reincarnation. He then takes this distilled list of cases and objectively analyzes them. His work has mostly to do with children who remember their past lives, because their memories are spontaneous (not artificially induced) and least likely to be tainted by any outside influences. He has also pioneered the study of birthmarks as they relate to past-life physical traumas.
While Dr. Stevenson cautiously adopts the phrase, "suggestive of reincarnation", in my humble opinion, I have less proof that my backside is currently pressed against the seat of my chair (not being able to see either directly), than he has of reincarnation. Don't take anyone else's word for it, read the original studies yourself, because most of the skeptical criticisms consist of ill-informed sophistry.