This is a bare-bone demonstration of how to check if the current user Likes your application, using Facebook Graph API.

• Login, then click the Like or Unlike button to toggle liking/unliking this application.
• Click the Check Like button after clicking Like or Unlike and the result reflect your choice (the result will be displayed in a JavaScript dialog box).

 
The write-up for this example can be read here:
/blog/2010/11/facebook-open-graph-api-authenticating-in-iframe-applications