To stop auto posting/publishing Facebook applications recent activity feed to your News Feeds, just follow the steps below:
1) Click the Account drop down menu located at the top right area (as per new FB Home Page, updated February 2010), then, go to Applications Settings, as shown below.
*Application Settings - Recently Used page (as in the snapshot below) will then be loaded, listing all the applications you use in Facebook (example: Farmville, World Cafe, Mafia Wars, etc.). The application with the "X" button at the right column are those applications that you've previous approved to be bookmarked and have access to your data; clicking the "X" button will stop the access to your Facebook data and the application will be removed from your profile, bookmarks, and Applications Page (in the list below).
2) In the Applications Page, click Edit Settings of the application you want to stop posting /publishing recent activity feeds. The Edit Application Settings pop-up window will then show with the Bookmark Tab as default. You can also uncheck that option if you like to remove the application from your bookmark icons.
3) In the Edit Application Setting pop-up window (as shown below), click the Additional Permissions tab, then UNCHECK "Publish to streams". That action will then stop auto posting/publishing of a Facebook application's recent activity feed to your News/Live Feed.