There is information on how to grab Real Audio streams from internet radio stations and convert them into .mp3 files here: HowToRipRealaudioStreamsToMp3.

This requires you to know the rtsp-protocol URL of the stream. Stations do not usually list their URLs, but embed them in .ram or .smil files. These can easily be extracted (there are instructions on the How To page) - but for convenience, the live streams of some popular major stations are listed below. Plus some random less-major stations!

Live Streams

NOTE: These live streams are what is being broadcast at this very moment. Many stations also archive some of their content and make it available on demand. Follow the How To page instructions to extract the URLs of archive content.

Please feel free to add any others.

BBC Radio Player

To stream from the BBC Radio Player, use the base address of : rtsp://rmv8.bbc.net.uk/<<BR>> And then add the path of the show as linked to on the player after the question mark.
e.g. If the Radio Player shows this link :
http://www.bbc.co.uk/radio/aod/networks/radio1/aod.shtml?radio1/anniemac
The RealPlayer stream link would be :
rtsp://rmv8.bbc.net.uk/radio1/anniemac.ra

For World Service, you need to change 'wservice' to 'worldservice'.