Developer: AOL Inc.
Price: $2.99 Download on the App Store
AOL Instant Messenger for iPhone is a fine product, and works just the way you would expect it to -- with one major flaw: unless the application is open (and currently you can have exactly one application open at a time), you don't get alerted when you receive a message.
How and when Apple will fix this remains to be seen. They have announced a change to the way they will handle "push technology", and in particular, allow apps to push messages to the Phone in general, even when they are not active -- starting around November. But with the high number of bugs and problems with MobileMe and Apps crashing, i wouldn't hold my breath.