Buddhists actually do think it ends eventually when your body is no longer connected to the material possessions which ties souls to the earth. That reincarnation is actually not a good thing b/c it means that you have yet to release all your desires and such which are earthly and that souls that life is torturous until you are able to release what is unnecessary and become enlightened. Those that are truly enlightened are no longer tortured and their souls are not reincarnated.
kahljorn 
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