AIM comes in both pay-with-no-ads ($2.99; direct iTunes link) and free-with-ads versions and both versions support push notifications. Beejive costs a hefty $9.99 (direct iTunes link), but connects you with a whole slew of different chat platforms. I’m sticking with the free version of AIM myself. One note, and this happened with both the Developer Preview version of AIM and this version: accessing Contacts sometimes crashes the app.
As I said yesterday on Twitter, I’m really looking forward to a Twitter client for the iPhone that takes advantage of push to give number count on the icon indications of @replies and that does push notifications of DMs. With that, I could turn off the SMS notification on my Twitter account.
Also, if you’re a iPod touch owner with the 3.0 update, then these push notifications should work fine for you too.
UPDATE: The free version of AIM for iPhone doesn’t support landscape typing / chat. LAME. Paid version supposedly does, but at $2.99 why not just spend a bit more on Beejive and have multi-platform chat?