I was talking about the Facebook messages, which are very similar to email. The App invites are pure spam, so they can simply be ignored. Spam is only a problem when it gets mixed in with something useful.

And unlike email there is no way to automatically filter most of it.

There's a greasemonkey script called UnFuck Facebook, which does exactly that - It hides all app things and auto ignores apps sent to you, hides all Facebook ads and makes it look very clean in general.