For several years now, I must have read a little less than a dozen books regarding cases about reincarnation. The most famous researcher of the subject, Dr. Ian Stevenson, had collected minute detailed evidences around the world, most of them were from Eastern Religious countries. His intention was not to prove or disprove the existence of reincarnation, his was to use rigorous scientific method to gather data to explore the paranormal phenomenon such as reincarnation.
Although I have no personal knowledge or experience about reincarnation either from family, friends or colleagues, I would not discount the possibility of its existence given many volumes of books detailing the incredible synchronicity even the best novels would be pale in comparison in its plot and intricacy.
Have you ever had a sense of Deja Vu? I remember when I was only five or six years old, sometimes, I would be playing intensely and suddenly I would look around the house, sky or just some building structure like a column, I would have a vague sense of familiarity, like I had been there before. Usually this could happen to young children since they have just freshly arrived from the other side. They have still retained not too distant memory of their past life.
For the western religion of Judeo-Christianity, the reincarnation used to be considered a devil's act, the concept was clearly rejected. But I suspect with the global infusion of knowledge and wisdom from the Eastern philosophy, the idea is gradually being accepted if not in your local churches but at least for family and friends who have been intimately affected by its occurrences.
Reincarnation holds the notion that some essential part of a living being can survive death in some form, with its integrity partly or wholly retained, to be reborn into a new body.
The book that I read recently about reincarnation is "Return From Heaven" from Carol Bowman. The stories are engrossing and fascinating. Whether you believe it or not, there are some good books out there for the subject if you are interested in making your own judgement and conclusion. May be you just want to entertain yourself with this wild idea.