According to TUAW, Tap Tap Revenge is the first app to have been updated to allow push notification.
If you are running OS 3.0, upon launching the new version of Tap Tap it will ask you for permission to send push notifications to your device. If you allow them, a new category called Notifications will appear in your device’s main settings, which will allow you to toggle push notifications on or off. Additionally, it appears that each app will have individual settings for badges and alerts.
While the type of notification you can receive hasn’t been confirmed yet, it is safe to assume that you may be notified when other users want to challenge you. Tap Tap probably won’t send any notification until the official release of 3.0 in 2 days.
Until June 17th, I believe we’ll see more and more of these app updates allowing push notification. Apple most likely wants some “big names” to be ready to push notifications when 3.0 becomes available for download on Wednesday.
Update: I just found this video that confirms that the notification system is for challenging friends.