You can find URLs to MP3 streaming music using freeware URL Snooper. And you can download them with your browser or any download manager.

You may also find some other methods in the following FAQ:
FAQ: How to record/download/capture/save Adobe Flash .FLV video and MP3 audio HTTP stream from embedded player

Replay Media Catcher can perfectly record HTTP .mp3 streaming music from jango.com:
Tutorial: How to record streaming music from Jango with Replay Media Catcher