If you get the Blackberry radio player it should. Last time I borrowed a phone and looked it seemed to be rolled into the general updates. It is also supposed to support aac+v2 streams, but I have not been able to test it to make sure. The mp3 streams should play just fine. Make sure to check your contract and make sure that radio streams will come from your data plan and not phone minutes. Pretty much all the companies have now done this but it is worth checking.
Nokia phones also support playing Shoutcast streams and are said to support aac+v2 streams. You need to browse to the Nikia website and download the Nokia player. Then you can play the streams listed with Nokia, not sure if you can type in a station that is not listed.
Your mileage may vary!