TweetMic [$0.99 - iTunes link] puts a whole new spin on Tweeting. With TweetMic you are basically able to Twitter small podcasts via this application. What happens when you use TweetMic is you record a message via the iPhone's built in Mic, you can play it back or post it with a short Twitter message.
Once you "Publish to Twitter" the application uploads the recording to its server and attaches a link to your post, so when your followers receive the tweet, they will see the link and the website it brings up will allow them to play the message via a computer or an iPhone.
Of course having WiFi of 3G will be better than using an EDGE connection when uploading you messages.
If you want to add audio recording to your Tweets, then this is definitely the best option out there. If you check it out, let us know what you think (or record a message for us on Twitter!)