I don't use Twitter as an immediate type of communication. I generally don't receive direct messages from people that I know, as I know that other people do. I still see Twitter as a passive communication medium.
Boxcar is an iPhone application that enables Apple's push notifications to be sent when your Twitter account receives a direct message or a reply. At first I didn't see that this would be useful for me. But then I remembered that I have installed WHSTweet on the two Windows Home Servers that I maintain. This add-in enables the server to send Twitter messages when the server has an error or warning.
Using Boxcar with WHSTweet is a perfect combination. Now my phone will let me know as soon as my server has a problem. There is less of a chance that I will miss the tweet from the server now.