A friend of mine kept asking me how the heck to remove or hide notifications from people who they're friends with who play lots of Facebook games. I was stumped but also didn't do much research aside from trial and error within Facebook's notification settings. No luck. When I Googled it this morning, it led me to a post (will fill in URL later) that showed how do it.
To do it, you go to your notifications page and click the "x" all the way to the right of the notification. From there you edit that app's settings (even though you don't even have that app) and choose "Never" for how it notifies you.
Here is the two step process on how to do this: