Ask Al: Help! My email address is being used in spam! What do I do?

Evan writes, "Hi Al, My email address has just been compromised and now I am receiving hundreds of System Administrator and Mail delivery failure notices sent to my inbox from all those poor people who have received unwanted spam from my address. I noticed your name on the web when I went searching to find out how and if I can stop this happening and was hoping that you might have some ideas other than changing my email address?"