This should have been thought of earlier. Wiibrew dev Scanff has released WiiRadio, a ShoutCast stream player that will allow you to listen to thousands of radio streams from the Web. To install, just copy the "radiow" directory to your SD under /apps.
This is only the preview version, so don't be surprised if there are hiccups, lags, or even crashes. Still, it's a good idea, and a great start to what could be an awesome app. Hopefully we'll see more updates from Scanff soon.