Just click the Hide button next to one of the offending notifications, and you will be given the option to hide notifications from that application. Even better, this also stops the notifications from appearing on the Facebook mobile site, iPhone application and third-party readers such as TweetDeck.

Thanks to Darren for bringing this to my attention.

There’s also the option of switching to Facebook Lite, a back-to-basics version of Facebook which does away with applications altogether.