Look in the What You Get Notified About section. Next to App Requests And Activity, click Edit and uncheck the apps you don't want to see. You can do the same for Groups, Tags and Friends activity.
While you're here, check the How You Get Notifications area. If you're buried in notification email, for example, you might want to turn it down a notch.
Have an installed app that won't stop bugging you? You might just want to remove it completely. Or you can turn off every app at once. But I should warn you that this setting can dramatically limit what you do on the site.
Click here to find out how to get total Facebook app privacy with one setting.
Notifications can be a pain, but maybe you want to filter other types of updates from your news feed.