The Mirrorball Man wrote:
The transporter KILLS you and then creates a perfect duplicate of you somewhere else, a duplicate who has every single one of your memories except the moment of your DEATH. That's why people in the Star Trek universe think that transporters are safe. It's because people DIE every time they step onto that thing, but they can't warn anybody.
This is my greatest fear, and exactly why I'm always warning people not to teleport. Even if "you" have done it a hundred times, the current version of you should avoid doing it again.
To my knowlege, the problem was first discussed in SPOCK MUST DIE (1970) by James Blish. He defined the transporter process in such a way that there was no doubt you were being re-created at the other end from scratch, not moved intact.
In TNG they defined transporting differently: a subspace carrier wave somehow acted as not just an information superhighway (instructions for your reassembly), but also as a physical highway for sending your actual subatomic particles.
Even so, I would fear that the new newly assembled you might be a copy who only thought he was the same old you.