Robin Hanson and Bryan Caplan are blogging one of the most fun arguments they've had, or at least one of the ones I enjoyed most at lunch as a grad student.
Suppose you're scanned, atom by atom, and a replica of you is made. Hanson then says '"me" got bigger'. The replica shares all of your memories and purposes; it seems pretty reasonable to view it as an extension of you. I'm with Hanson up to this point.
Hanson then claims to be indifferent between whether he or his replica is shot following replication. Either way "me" gets smaller. So Robin would have no problems in stepping into a Star Trek teleporter: the teleporter destroys the current instance of 'him' but creates an identical new instance elsewhere who materializes remembering having stepped into the teleporter. I'm with McCoy: there's no way I'd step into the teleporter. Shuttlecraft only, unless the alternative is that the only instance of 'me' otherwise would be destroyed (yes, I'd teleport away from the planet that was imploding if the shuttle couldn't get there in time). And then Hanson would needle by asking why you're ever willing to go to sleep.
Robin and Bryan are currently arguing this with respect to cryonics. Robin's happy to go for cryonics even if it only gives the chance of having a simulated upload of his brain run on a computer sometime down the line; Bryan doesn't think that's good enough. I'd take the upload over nothing, but would still prefer waking up thawed. And Robin would of course demolish that line of argument: whatever is woken up a century or two from now will only be 'you' to the extent that the neurons are in the right positions with the right charges, so there's no particular reason to prefer that the physical instance of your current brain is woken up or some replica of it or a neural net scan that's running as an upload on a computer. In all cases, something would wake up with a memory of having been 'you'.
If you're a materialist, it's hard to avoid Hanson's conclusion. But I still want to give a higher priority to the current instance of 'me' than to any potential extensions. I remain a "me-utilitarian", where higher weights are placed on instances of 'me' closer to the current instance.