I think that the key word that requires understanding and definition here is "research", which to me means studying credible sources regarding a particular subject. Although it need not be strictly empirical or repeatable, I think it needs to be as credible as possible. So when it comes to the most valuable research pertaining to Reincarnation, it is common knowledge that Dr. Ian Stevenson has done more quality research toward the advancement of Reincarnation studies than anyone else in history. Giving Carol Bowman's work a close second, Dr. Stevenson's work has been the most successful because he has conducted intensive inquiry among children whose conscious memory could not have been as affected by media and technology as those in more developed societies. When you come across a child in a south Asian village who claims to have been a deceased person from an entirely different caste and a village never visited, yet one who knows specific relatives of that previous person, exhibits birth scars that correspond to that previous person, and even knows who killed him; then you have what I would call an extremely interesting piece of evidence, which—when combined with all the thousand or so cases Dr. Stevenson has amassed—gives the strongest evidence for the possibility of Reincarnation.
I would agree with others that there is much more to proving Reincarnation than one form of research, for there is much to be said in support of personal experience, logical reasoning, knowledge of human nature as well as other paranormal research. As most of us already know, there is no way to empirically prove that Reincarnation exists beyond a reasonable doubt. But, when it comes to convincing skeptics that Reincarnation does exist, I think that there is no research more potentially convincing than the research conducted by Dr. Ian Stevenson.
In one sense, it is regrettable that technology has so effectively connected the populations of the world; for it is becoming nearly impossible to find a child, nowadays, who has not been somehow influenced by a myriad of influences that can dilute possible past life memories. When they utter strange comments regarding things they should not know, it is hard to discern whether they acquired such information in this life or in a past life. For this reason, I think it is becoming increasingly difficult to conduct the kind of research that Dr. Stevenson conducted a few decades ago.