One of my friends asked me for help to "get rid of that joke", specifically CityVille. I thought - why not make a step by step how-to guide about this process because of FB's broken user interface? So here it is.
1. Game Requests.
2. Game Requests expanded.
Here you have an option to accept or to hide each request. If you are to get rid of it, obviously you need to hide it. Click on "X" button (see in pic on right). Request will be hidden and instead you will see some text saying you did what you did (hid a request) and some link with a keyword "block" in it. Sorry, no pic for that link.
3. Game News Feed
What is more annoying than requests are zillions of news feeds from apps especially if your friends are hyper active Flash gamers. Here you can see one of those news feed items. When you hover your mouse pointer over a news feed item, a small "X" button appears on it's top right corner. Click on it and choose "Hide all by [APP]". Do not choose hide all from friend or you won't see his status changes.
4. Block the App
First of all, find a game's official page. A bookmark menu on your top left with a name of the app will not get you to the game's page, it will get you to the game itself. It is not what you need. On the very top of FB page is search field where you can search just about anything you can think of. Type there the app's name. One of the first shown should be the one you need.
Beware of the scam pages (you know, the ones promising you "The Brand New Unreleased Golden Cow That Will Instantly Turn Your Farm To 100x100!!! It's Working!!!11one"..) Yeah, right.. Read more on The FaceGamer's blog.
When on the right page, look for a button "Block app". Click it and enjoy freedom from flash games! I will not cover how to unblock and unhide games. Trust me, it's not worth it. There are many much better things to waste your precious time on, like commenting this post just to say 'thanks'.. ;)