For those of you who haven't seen it, the movie The Prestige (IMDB: http://www.imdb.com/title/tt0482571/) deals with this topic of transient existence of people, albeit in the context of magicians and science. It's a very good movie, to boot.
Yea, I was excited when I first saw that movie. The main character completely failed to understand what was going on: "Would I be the one transported, or the one in the tank?" He was both, but the selection bias of being able to ask that question would make him seem very lucky.