It took me a few minutes to remember where I saw it, but there it is. An episode of the Outer Limits called Think Like a Dinosaur has dealt with exactly this question. It is based on a novelette by the same name by James Patrick Kelly.
This issue is also mentioned in Ilium/Olympos by Dan Simmons, where the Earth is covered by a network of "fax nodes", which can instantaneously "fax" a copy of a person to another pointnode, destroying the original.