kulturradio.de uses Icecast HTTP MP3 streams as well as Windows Media streams for its live broadcasts.
To download Shoutcast/Icecast MP3 streams you can use almost any program. There are lots of
Shoutcast stream rippers including freeware StreamRipper plug-in for Winamp.
As for on demand streams, kulturradio.de uses RTMP protocol. I didn't have any problem downloading as well as capturing them with
Replay Media Catcher 4 and
WM Recorder 14. I was also able to extract MP3 audio from downloaded/captured FLV files using Replay Media Catcher.
You can also download RTMP streams with freeware
CooJah + Blader,
Orbit Downloader,
StreamTransport,...
And you can try to capture RTMP streams in real time while you listen to them using freeware
CooJah (without Blader), Orbit Grab Pro.
If you use Linux, try rtmpsrv or rtmpsuck.
Related:
FAQ: How to record/download/capture/save Adobe Flash .FLV video RTMP stream from embedded player
How to record rtmp:// flash video .flv stream from embedded Adobe Flash Player