I just searched Google and found 1.fm It looks like it will play Shoutcast streams. So, try downloading TuneWiki (I like this one, it will play shoutcast and last.fm and your music and videos too and do YouTube searches) or DroidLive (plays shoutcast)
In TuneWiki, you click on the icon of the microphone, then select Shoutcast, then Search. I entered 1.fm and I found some 1.fm stations. If you press Home and the TuneWiki disappears, you can start it again and press on the bottom right icon that looks like red headphones and it takes you to the Now Playing screen again.
Also, when you start TuneWiki again later, you can go to Recently Listened To and find your station again quickly.