I'm not a spammer

tfinniga writes: A spammer has recently started using my domain name as "From:" addresses when sending out spam. I'm worried about my domain being blacklisted, and I'm annoyed by the bounces — I'm getting about 1000 bounce messages a day. Unfortunately, I give out a different email address to each site I visit: [e-mail], [e-mail], [e-mail], etc., and the spammer is using a different address for each mail, so simple address filtering doesn't work.

What is the best way of avoiding being put on a blacklist, and dealing with the flood of bounces?