I'd like to have a contest hosted my Website and to enter it, the user will have to "Like" my Facebook Page and do other various actions while logged in my site... Anybody know how you can "track" the likes on Facebook and how you can associate the likes with authenticated users on your Website?
There are several ways to do this, depending on what FB API you'd like to use. You could for example call up the user's information: http://developers.facebook.com/docs/reference/api/user/ (Graph API) You could also do a FQL query, this might help you.