This updated version of AOL's AIM client for iPhone supports the push notifications introduced in iPhone OS 3.0. It was the first IM app to have that feature. AIM leaves you logged in for 24 hours (by default) after you exit the app, and when you receive messages, you'll receive push notifications about them.
This app also lets you send SMS text messages to the numbers in your iPhone's contact list, partly bypassing AT&T's own messaging system. Another cool feature: like Where and similar apps, AIM can broadcast to your buddies where you're located by using the phone's GPS.
AIM for iPhone is available in two versions: a free one (direct iTunes link), and a pay one which costs $2.99 (direct iTunes link). The free one is ad supported, and it doesn't presently have a landscape keyboard option, which is arguably a tough pill to swallow.