Reincarnation, or metempsychosis, is the transmigration of souls. It is a pagan concept, alien to Judaism, Christianity, and Islam. Basically it contends that after death, a human soul can return to earth in another human body or, if the person was evil, into the body of an animal. The notion of “previous lives” is a variation of this belief that souls are somehow recycled after death.
Christians—Catholic, Orthodox, and Protestant—strongly repudiate this idea. Genesis tells us that God created Adam and Eve with a body and soul, and both were good. Jesus Christ took on a human nature which meant in addition to his divine nature, he also had a human body and soul, both uniquely his own. He suffered and died for each and every one of us, body and soul.
If an evil life can be atoned merely by coming back in another form or by using another body, then there is no need for redemption or salvation. Christianity says otherwise. One person, one body, and one soul. The doctrine of the resurrection of the dead clearly conflicts with reincarnation. If multiple bodies could be used by one soul, which resurrected body gets the soul at the end of the world? Despite the hallucinations of some Hollywood celebrities, mainline Christians, Muslims, and Jews place no credence in reincarnation.