Alternatively, in the small notifications roll-up window on the bottom right, an "x" will appear as you hover the mouse pointer over individual notifications. Clicking on it will remove any further notifications from that application.
Finally, for additional fine tuning, you can click on Settings in the main menu, then on "Application Settings". Choose "Authorized" from the drop down menu. Many applications actually have quite a lot of privileges. For example, some are able to "Access my data even when I'm not using the application," "Send me emails" and "Publish recent activity to my wall." From here, you can turn all of those off without actually removing the application. If you want to really make sure the application will never bother you again, you can completely remove it by clicking the "x" next to its name.
Now, you can do the same for Updates. Click on "Updates" in the menu on the same page (you can reach the page by clicking on "Inbox" from the main menu), and then click on "Updates Settings" on the right. From there, you can control which updates you receive. Save changes, and you're done.
That's all! Enjoy your new, nag-free Facebook.
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