Easily the most useful push app Apple's let through the gates, Prowl lets you forward any Growl notifications from your Mac or PC—everything from Mail to IM to Torrent downloads to Tweets—directly to your phone.
For anyone who doesn't know, Growl is a free system-wide notification system for Mac OS, and as of a few months ago, Windows. Any app that runs through noteworthy events—download completions, news messages, etc—can use it to display an onscreen message. Prowl simply bridges your desktop notifications with your phone. Practically, this translates to push everything, if you care to spend enough time setting it up. Some folks are even offering plugins that let you use the app without leaving Growl running.
From The App Developers: Prowl is the Growl client for iPhone OS. Notifications from your Mac or Windows computer are sent to your iPhone or iPod touch using push. Prowl has an extensive API, which allows your scripts to integrate beautifully.