(Note: For the New Age section the process of selecting opinions based on authors education and experience- general credibility- was significantly more difficult compared to the other worldviews. If you are able to suggest sources that include also this type of information please post a comment or send a note. Thank you.)
According to Curt John Ducasse, professor of philosophy at Brown University, author of different books on the subject, alleged evidences of reincarnation are past life memories (a person possessing self-referential veridical information about a formerly existing person), similarity of physical features, similarity of character and personality, similarity of practical and theoretical skills, similarity of self-perception (a person perceives himself as a formerly existing person perceived himself), the existence of widely divergent degrees of moral, spiritual, intellectual and practical skills, and finally the fact that reincarnation makes human suffering or the various inequities of life intelligible.
The same author said that the virtue of the pre-existence hypothesis is that it is compatible with the belief that the universe is overall a just place, for the inequities in life would be explained by a person’s own actions in the past, not bad luck.
See references about the author here.
Victor Zammit in his book ‘A lawyer presents the case for the afterlife’ said:
“The modern evidence for reincarnation comes from past life regression, spontaneous recall of past lives, transmission of information from the afterlife, Theosophy, Edgar Cayce, and recent translation of Sanskrit texts. However in keeping with the scientific emphasis of this book, concentration will be made on past-life regression, and spontaneous recall of past lives.
Some who do not accept re-incarnation argue that the evidence can be explained by possession or spirit influence. That may be so. It is not the purpose of this book to argue either for or against reincarnation—simply to present some fascinating evidence. But whether you take the reincarnation view or the spirit possession view, the evidence builds more strongly the case for life after death. … When critics are confronted with this most convincing evidence for reincarnation, they try to explain the results away. They claim it was caused by extrasensory perception, by telepathy or clairvoyance… In the alternative, skeptics have argued, the whole thing could be fraud, cryptomnesia, spirit possession, fantasy, paramnesia, inherited memory/collective unconscious. Let us examine, as Ian Stevenson did, each of these arguments in turn (Stevenson 1977).”
See detailed examination by the same author, at: http://www.victorzammit.com/book/chapter24.html
On a humorous tone, for those concerned how well they are doing on the reincarnation side so far here is a link claiming to tell in which form one is to be reborn upon death: http://www.reincarnationstation.com/