Similar to Teleportation?
A big concern about teleportation (which became famous in Star Trek "beam me up") is that the person being "beamed" actually DIES is DESTROYED then replaced by an exact copy, the copy has all of his memories and has no way of knowing that he is only a few seconds old while the earlier version is dead. I had this discussion with a friend once and he insisted that if a copy is exactly the same then its "you" in every sense of the word that matters.
Well is the cloning like that too? I mean whats the point of cloning yourself (unless you just want to leave a legacy) if the clone just replaces you but you are still dead? Maybe its more of a philosophical question than a scientific one?