I want to block app and game invitations once and for all in Facebook. How can I do it so they cannot disturb me anymore?
You can block app invites from specific friends by clicking on the gear menu in the upper right corner and then Settings, Blocking, and entering names under Block app invites. You can block specific apps from this same page under Block apps. If you do not use any Facebook apps or games and want to block them all from seeing any of your information or sending you invites, you can turn off Facebook Platform completely by going to Settings, Apps, Apps you use ... Edit, and then clicking Turn Off Platform.
You cannot block all Facebook game invitations.
- Block game invites to a specific game
- Block game invites from a specific friend.
Some background: Facebook derives a significant portion of their revenue from applications on the platform, especially those that are games. By allowing people to completely opt-out of games at all they'd be shooting themselves in the bottom-line.
In summary, the reason that you cannot opt-out from all games is that Facebook doesn't have a feature that allows you to do so since that feature could easily kill a good portion of their revenue.