According to iphonestalk, they haven’t seen many applications that support push notifications but apparently now AIM does and delivers instant background messages even when not running.

Apple doesn’t allow the iPhone to run background apps and as a workaround iPhone OS 3.0 supports push notifications which send SMS type alerts direct to the iPhone even when app is running.

Overall, the push notifications seem to be working really well, although when logged into AIM via the desktop client no notifications came through but once logged out the push notifications were again making their way to the iPhone.