If you or any of your Facebook friends have signed up for the "Farmville" game application, you might receive regular "Farmville" posts and activity updates on your Facebook Wall and in your Facebook homepage news feed. Facebook allows users to remove applications from the Facebook Wall and hide application posts, updates posts and updates on the homepage news feed. Remove "Farmville" content from your Facebook pages by removing or hiding the application.
Instructions:
1) Sign in to your Facebook account.
2) Click "Account" in the top navigation menu. Select "Account Settings" from the pull-down menu. Click the "Applications" icon in the left-hand menu.
3) Click the blue "Edit" link beside "Farmville" in the list of applications on the Application Settings page.
4) Click the "Remove" link next to the "Post to My Wall" setting option. This removes permission from the app to post to your Facebook Wall.
5) Click the "Home" link in the top navigation menu. This opens your Facebook homepage with the news feed in the center of the page.
6) Scroll to any "Farmville" post or update. Hover your mouse pointer over the "X" icon beside the post. Select "Hide All by Farmville" in the drop-down menu. This removes "Farmville" content from your news feed.
Tips & Warnings
Repeat this procedure to remove activity updates or posts from any game or application on Facebook.
Source: eHow