There's no good evidence for any kind of a literal reincarnation.
The kids who "remember" their "past lives" were likely led to believe such.
On the other hand...
There are unexplainable aspects of consciousness, which I've seen. They might be mass suggestion, they might be universal consciousness, but for now they're unexplained.
Awareness itself brings about "rebirth," in a sense.
But literal reincarnation?
I don't think it's necessary.