Farmville is a Facebook application that can lead to a ton of posts and spam. Expect frequent messages from Farmville letting you know that a friend has visited your farm or that your plants have been fertilized. There is no delete option on the Farmville application itself, however you can easily remove the game from your Facebook account.
Instructions:
1) Log in to your Facebook account.
2) Select the "Account" menu from the upper right corner of the page and click "Privacy Settings" in the drop-down menu.
3) Scroll down the Privacy Settings page until you come to the Apps and Websites section. Once there, click "Edit Settings."
4) Click the "Edit Settings" button next to the section titled "Apps you use."
5) Locate the Farmville app in the list and click the "X" to the right of its name.
6) Click "Remove" in the confirmation pop-up window to delete Farmville from your Facebook account.
Source: eHow