Reincarnation was actually taught by the Buddha. Reincarnation and Karma go together like peanut butter and jelly. If you do really good things, everything in your life works out perfectly and after you die, you get to be reborn into a wonderful family who will do their gosh-darndest to help you along your path to Buddhahood. If you do bad things, your life is terrible and you are miserable and when you die, you'll come back as some sort of poop-pushing beetle1 or something equally awful.
Once upon a time in ancient India the Brahmins ran the whole shebang. They came up with the idea of reincarnation. It was based on the caste system. It's sort of a primitive monopoly system. If you were born the child of a Brahmin, you were a Brahmin. That's the only way you could get into the club. It was your job to learn all of the holy books and after you were done, you were qualified to do all of the religious ceremonies. Strangely enough, all of those ceremonies involved giving a great deal of wealth (in the form of clothing, cattle, dry goods, and gold) to the Brahmins!
Now, if you happened to not be a Brahmin, this system would seem extremely screwed up and one sided. You might get resentful. You might start a revolt. If you were a member of the warrior caste, you might want to go over to those guys and lay down a different system with the edge of your sword. Nope, didn't happen. See, the caste system was created by God, and the Brahmins were just doing their duty. But, and here's the way the system kept working (and still works); if You did YOUR duty, then one day you could be reborn as a Brahmin! What a sweet deal! Just build up enough good karma and you can be in charge of the show!
In Buddhism reincarnation is a contradiction. If there is no permanent eternal self, then what is there to be reborn? Some Buddhists will namby-pamby around the issue saying that it's the karma that continues, or it's mind. What it basically boils down to is the refusal to man up and admit that if there truly is no soul then The Buddha was lying or wrong about reincarnation. If there is a soul, then The Buddha was lying or wrong about impermanence. Reincarnation is an idea best left back where it belongs; as a con-job from the dark ages.