As a refresher, Apple doesn't allow the iPhone to run background applications. As a workaround, the new iPhone 3.0 supports push notifications that send SMS-like alerts straight to your phone even when an application isn't running. That means that you get the benefits of background apps with none of the battery drain.
I tested out the new AIM (free version) over the course of the day, and overall the push notifications seem to be working really well. I wasn't receiving notifications when I was still actively logged into AIM through my desktop client, but once I signed off at my desktop, the push notifications started making their way to my iPhone.
As with all apps supporting push notifications, you have the option to toggle the in-your-face level of the notifications, selectively enabling sounds, alerts, and badges. If you've been playing with AIM or other push notification-supporting apps since the 3.0 update, let's hear how it's been working for you in the comments.
Note Unfortunately the AIM client only supports, well, AIM. If you're looking for multi-protocol support and push notifications, the $10 Beejive looks like a great (though expensive) solution.
AIM (Free Edition) [iTunes App Store]