Question: "What does the Bible say about reincarnation?"
The concept of reincarnation is completely without foundation in the Bible, which clearly tells us that we die once and then face judgment (Hebrews 9:27). The Bible never mentions people having a second chance at life or coming back as different people or animals. Jesus told the criminal on the cross, "Today you will be with me in paradise" (Luke 23:43), not "You will have another chance to live a life on this earth." Matthew 25:46 specifically tells us that believers go on to eternal life while unbelievers go onto eternal punishment. Reincarnation has been a popular belief for thousands of years, but it has never been accepted by Christians or followers of Judaism because it is contradictory to Scripture.
The one passage that some point to as evidence for reincarnation is Matthew 17:10-12 which links John the Baptist with Elijah. However, the passage does not say that John the Baptist was Elijah reincarnated but that he would have fulfilled the prophecy of Elijah's coming if the people had believed his words and thereby believed in Jesus as the Messiah (Matthew 17:12). The people specifically asked John the Baptist if he was Elijah, and he said, "No, I am not" (John 1:21).
Belief in reincarnation is an ancient phenomenon and is a central tenet within the majority of Indian religious traditions, such as Hinduism, Sikhism, and Jainism. Many modern pagans also believe in reincarnation as do some New Age movements, along with followers of spiritism. For the Christian, however, there can be no doubt: reincarnation is unbiblical and must be rejected as false.