While the request permissions pop-up is great for avoiding the instal of scam applications, what do you do if you have already given the spamming application access? Well the first step is to check your profile to see if the app has changed your status. If it has, be sure to clear your status so your friends don't get scammed as well.
After checking your status, move on to your wall. In the case where the app has posted to your wall, don't just delete the wall post. Instead, click on the "x" to the right of the post and select the option where it says "remove" and then the app name. After doing that, then remove any subsequent wall posts from the app that may not have been deleted. To be sure Facebook removed the application completely, be sure to go to your privacy settings, click "edit settings" for applications and websites, and then make sure that the spam app you deleted is not there. If it is, click the remove button and then click the "x" to the right and confirm you selection.
You now have successfully removed the spam application. But before considering yourself finished, be sure to check the rest of your profile to ensure that the app did not automatically "Like" certain pages or change your interest.
If you have followed all of the steps above, you will be able to clean up any mess that a spam app has left, as well as hopefully avoid future spam applications.
(Image via Flickr user Franco Bouly)