How do I turn off App Store notifications in Mountain Lion The App Store on Mountain Lion pushes update notifications through Notification Center. Unfortunately, this also happens for users that are not system administrators (and so cannot run the App Store). How can I turn this off?

Notification Center has preferences, where applications can be vetted, but App Store does not appear in this list.
You can now simply go to System Preferences > App Store, and turn off "Automatically check for updates."

No messing with firewalls, and just works with App Store. So just remember to check every now and then manually to find out when you have updates!