I remember part of an episode of the Big Bang Theory where Sheldon speculates that matter transporters like those used on Star Trek wouldn't so much move a person from one place to another as kill the person being 'beamed' and create a clone with his knowledge/memories/personality on the destination site- has anyone on any of the Star Trek series expressed concern this might happen to them?
Actually, yes, there were people within the Star Trek universe who had this particular fear.
The matter is fully confronted in the Next Generation graphic novel Forgiveness by David Brin:
There, he introduces a 21st Century scientist who invents the transporter, Colin Blakeney. Blakeney faces fear and hatred from groups who believe that once a person steps through the transporter, the result is a soulless copy.
If TV is more your thing, there is the Enterprise episode Daedalus. Confusingly, we meet another inventor of transporter technology (Erickson) – and while TV canon trumps EU, this is usually explained as Blakeney giving up and falling into obscurity for Erickson to replicate the work and get the credit years later.
“There was all that metaphysical chatter about whether or not the person who arrived after the transport was the same person who left and not some weird copy,” says Erickson.
“Which would make all of us copies,” responds Trip Tucker, Enterprise engineer.
“I had to fight all of that nonsense,” replies Erickson.
It would seem, however, that by the time transporters are in regular use, this fear is almost non-existent, and the reality would seem to be that the transporters don't quite work that way, and no-one has this particular fear.
In Forgiveness, Blakeney accidentally transports himself to the future and encounters the Enterprise-E, and has this conversation with Dr Crusher:
“The transporter doesn’t just send information on how to build a copy of you," Blakeney concludes. "It sends you… soul and all.”
“Of course it does!” Crusher responds. “Do you think we could ever step into the thing, if we weren’t sure of that?”
Season 6 TNG episode Realm of Fear shows that transportees are capable of conscious thought throughout the process, indicating a continuity in the existence of self. While Barclay is afraid of transporting, of all the things he is afraid of happening to him, not being the same person after transport (and therefore being killed on the pad to be cloned elsewhere) is not mentioned at all.
While digging into this question, I found a rather excellent article from Ars Technica – Is beaming down in Star Trek a death sentence? – which reviews a whole lot of content (TV, movie and EU), along with interviews with the production team and real-world physicists.
“The way that the description of beaming is written, I would go for ‘you die and you’re reconstructed,'" said Michael Okuda, technical consultant for the various Trek shows and movies beginning with The Next Generation
So, it seems one of the chief technical contributors to the show would go with the death/recreation interpretation. However, he does also have this to say:
Okuda noted. “In the Star Trek universe, people are seen using the transporter on a routine basis, which suggests that however this concept is implemented on the Enterprise, it clearly does NOT involve killing the person. Otherwise none of those smart people would ever get near the thing,”
Rather than an imperative, this is the title of the first Star Trek novel written that was aimed at older readers. Written by James Blish, who wrote the novelisations of the original series, the opening scenes are described in Wikipedia as:
Doctor Leonard McCoy (erroneously nicknamed "Doc" instead of "Bones" throughout, for which Blish blamed an editor in one of his subsequent adaptation collections) and Engineer Montgomery Scott discuss McCoy's fear of the transporter. McCoy posits that an original person is killed upon dematerialization, and a duplicate is created at the destination. Scotty explains that the technology does not destroy the original object but causes every single particle to undergo a "Dirac jump" to its new location – and that converting a human-sized mass to energy would blow up the ship. McCoy is not convinced, and he wonders what happens to the soul in a transporter beam.