Is there a way to enable notification badges on the Galaxy S III? For example, when I have 5 unread emails, the email app shows a red circle with a 5 in it. Can other apps that I install do this as well?
Yes, other apps can do that, but it is up to the app developer to implement Notifications.
This morning when I grabbed my phone I had two different new email notifications (multiple accounts), a Facebook message notification, an app update notification, a Draw Something nudge from my daughter, and a notification that I had new podcasts downloaded in DoggCatcher.