I know of private shoutcast servers that transmit music and I would like to hear from my iPhone on the go
TuneIn Radio will let you add custom URLs (including ShoutCast server URLs) to your bookmarks list and stream from them. It will also keep your playlists in sync across multiple devices, record streams for, find local streams using your current location and more. You but it the app store. And when you're at your Mac, you can use their browser-based desktop app to keep listening and access your bookmarks.
To add a ShoutCast server as a custom URL use:
Once you add the custom stream to your bookmarks it should be available from any TuneIn Radio application or their web app.
I am not sure if the official SHOUTcast app lets you add private servers, but worth a try.
FStream is one of the best radio streamers and looking online, looks like it can open Shoutcast streams. I have used it for some other streams from local radio stations and a few other streaming sites and really liked it.
Finally, there is an app called Tuner Internet Radio that looks like it can open Shoutcast streams too.