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If you're in a pinch and need to use AIM, MobileMe, or .Mac chat, the AIM app for the iPhone is your best bet. It's a lot more stable than any of the web versions, even Meebo. The issue is, this app would be so much more useful if it could operate in the push capacity that Apple is taking advantage of for their own proprietary needs.
Having to have the application active to receive a message makes it difficult to do much more than log in, see who's on, see who responds when you message them, then log off or close the app. When you open it back up, you'll either receive all the messages at once, or find out that you've been disconnected.
It automatically remembers your login, so be careful with that. Plus, in the iPhone settings app, there will now be an option for AIM that will let you determine if closing the application signs you off and if the sound is on or off for this specific application. The application eats a lot of battery as well, so unless you're plugged in, consider sending that person a text or an email.
With other instant messaging clients now available for the iPhone and iPod Touch, the usefulness of this app is decreasing. If you start a conversation with a friend who you've set an alias for, you'll find that after a few messages back and forth they drop back down to being displayed as their screen name. While this doesn't change their alias when you log in on your computer, it is rather frustrating if you haven't seen anything but the persons alias in a long time.