Where is the "Become a Fan" Button?

The "become a fan" button does not appear on a page -

1. if you are signed into Facebook, AND
2. you are looking at your own page, OR
3. you are already a fan of the page you are looking at.

The "become a fan" button will appear ONLY if you are looking at a page that you are NOT already a fan of.

The same rule applies to the "become a friend" button on profiles.

Similarly, you will not be invited to "join a group" if you are already a member of that group.