I like to use the following: "A person tells the government that they saw a TV in the local pawn shop which is really theirs. They never asked the pawn shop owner for it back and they have no reason to suspect the pawn shop owner knows it is stolen. The government will then shut down the pawn shop without even talking to the owner first or having significant proof that the item was really stolen. Every phone book will be required to remove the pawn shop's phone number from it and maps will not be allowed to show the pawn shop. The pawn shop can then attempt to get their store back from the government but if it turns out that the item really was stolen then the government will not return it." In the analogy the pawn shop is a website, the owner of the item is the copyright holder, the item is copyrighted content, and the removal of the phone number and map info is dns-delisting and search-engine de-indexing.
I think the above analogy holds up fairly well and clearly demonstrates the ridiculous measures SOPA goes to. It's also much more easily understandable by non-tech-savvy people. Please tell me if it is not accurate in some way or is unclear.
Edit: If you want to add some sympathy, replace pawn shop with Salvation Army and TV with pair of jeans.
Technically the store isn't shut down it's only removed from the phonebook. At this point the analogy breaks down as that doesn't sound as drastic at all. However, on the web, being removed from DNS would be a death sentence to legitimate sites but ironically (and tragically) not for sites dedicated to copyright infringement.