Facebook has just announced and launched a new feature in their Requests page. A simple “clear-all” option for when you have lots of requests waiting on your Requests page.
I don’t quite understand why they didn’t also add a “accept-all” link right next too it. And while you are at it also add a “Make this my standard action” link.
Most people I know simply accept everybody who invites them. It is easier than finding out who everybody is and less risky than ignoring or denying invitations.