One of the most prominent features highlighted on the new iPhone OS 3.0 was the availability of push notifications, which for now can work as a band-aid fix given the lack of true multi-tasking on the iPhone platform. AOL's Instant Messenger (AIM) is one of the first apps to take advantage of push notifications, allowing you to get a pop-up when someone sends you a message regardless of what app you are currently running.
If you don't happen to use AIM but want Messenger or ICQ support, Beejive is another paid iPhone app that has been updated to use push notifications and can support multiple IM networks. As mentioned before, this is only a workaround to the true limitation of no background app support on the iPhone, but in the context of instant messaging, it's almost all you need.
Ultimately Apple will have to cater to the growing masses of developers and consumers that want true multi-tasking on the iPhone. But until their next-generation platform gets here, you can expect to see many more apps taking advantage of push support in the weeks and months to come.