A friend just sent me this link, which looks useful. There's also a video showing it in action.
Ignore all facebook requests button | One click ignores all applications / invitations http://www.ignoreall.com/
A button to ignore all facebook requests at once! One click ignores all applications, requests and invitations on facebook, group invitations and friend request stay!
Now we just need an auto-blocker. (I block each application when I see it for the first time because I'd prefer to only see each invitation once in my life.)
*UPDATE* More Facebook hints (how to make Facebook less annoying).