I would think that we would probably want to have cultural, ethical, and legal rules against infinitely copying yourself. For one thing, that leads to the rather dystpoian situation Robert Hanson was talking about; and for another, it would lead to a rapidly diminishing amount of variety among humans, which would be sad. One or two copies of you might be ok, but would you really want to live in a world where there are billions of copies of you, billions of copies of Von Neumann, and almost no one else to talk to? Remember, you are now immortal, and the amount of subjective time you are going to live is going to be vast; boredom could be a huge problem, and you would want a huge variety of people to interact with and be social with, wouldn't you?

I really think that we wouldn't want to allow an large amount of copying of the exact same mind to happen.