If you consult quantum physics, we know that electrons can be in two places at once(which really makes no sense) Source: http://discovermagazine.com/2005/jun/cover
If we apply the same logic (and much more advanced technology) into a teleportation device, we come across a strange question.
If we had a machine that can snap shot your every molecules and rebuild them into a different place(teleportation) would you still be there same person?
Even more fun to ponder: If we used that teleporter as a cloning devices and created two exactly identical(to the very last brain cell and atoms) would those two persons be the same person?