Many, many cases have come up and they say that someone remembered their past lives and had knowledge that they would never know. I know I can't seem to trace back my past lives, but that don't mean that it is a lie. I know people can fake it and I'm sure the media has a fake story out there
Simply put, there is absolutely no evidence that it happens. Those that say they had "past memories" are simply being a child, had a random daydream/regular dream, or accidentally over-cranked their imagination, just like the existence of God. However, the future may or may not have the ability to catch people's souls and stuff them into cloned bodies. We just don't know.
There is no evidence of reincarnation, those people who claim to 'remember' events from previous lives get from dreams using knowledge they have been taught from this life or make it up to attention seek. There is no conclusive evidence from any scientific experiment to suggest that reincarnation can be real.