For the short term, set up a filter to move any bounce messages to another folder, like your spam folder or possibly trash. Filtering out phrases like "failed delivery" or "Delivery Status Notification" should help reduce the unwanted clutter in your inbox. Usually backscatter drops off quickly. However, it is possible for the spam to go on for quite some time.
For long-term solutions, consider using another email address. Specifically, look into setting up an email service with Sender Policy Framework (SPF), an open standard that offers a technical method to ensure that incoming messages have originated from the proper domain. That verification can drastically reduce the amount of backscatter you receive.
As a final bit of advice, and I know this is obvious, don't fall victim to 419 fraud. Many times people feel violated when they do. It helps to know, though, that there are people who turn the tables on 419 scammers. Check out 419 eater for a good cathartic laugh.
This was first published in January 2009