You can subscribe yourself to public Google Groups. Follow the instructions below.
First, you can go to the Groups page in Google Apps, and browse all groups. Some of the groups may not be in the directory, so they may not show up there. The Group admin can either add themselves to the directory, or Support Central can do it for them.
Second, you can send an email to <group-name>+firstname.lastname@example.org and the request will be sent to the list owner for the membership.