CastCatcher Radio is on sale for 99 cents from now through 9 PM EST tomorrow night. 
It stores your favorite streams and plays AAC+ and Shoutcast/Icecast/mp3 streams. It works very well with high bit rate streams (provided your connection does, of course). AAC+ playback requires iPhone 2.2. It does work when the screen shuts off, of course.
Link.
Edit: price might still be updating -- give it a sec to show up on the app store. Thanks!
Edi2: Extended through Cyber Monday
It stores your favorite streams and plays AAC+ and Shoutcast/Icecast/mp3 streams. It works very well with high bit rate streams (provided your connection does, of course). AAC+ playback requires iPhone 2.2. It does work when the screen shuts off, of course.
Link.
Edit: price might still be updating -- give it a sec to show up on the app store. Thanks!
Edi2: Extended through Cyber Monday