If someone constructed an exact molecular duplicate of me, would I be standing here looking at him, or standing there looking at me? I doubt that there would be a strange double vision thing going. Far greater philosophers than I am have sweat blood over things like this, and I suspect the idea of a soul was arrived at partially out of mental self-defense.

When I go to sleep at night, the same brain wakes up in the morning. If my brain were transplanted into a cyborg, I'd still be in there. Make a copy of me? Where am I then?

Now, moving into the geek zone, I looked into this a little bit, and it seems that the Star Trek transporter concept does not actually destroy something and rebuild a new copy, but actually just disassembles the molecules and pipes them to a new location for reassembly. I take it significant amounts of RAM and processing capacity are required for this.

Does this change things? Who knows?

Safest bet: keep my brain in one piece.