For those of you that listen to Radio 1 over the internet, this might come in handy:
http://www.bbc.co.uk/radio1/wm_asx/aod/radio1.asx (low quality)
http://www.bbc.co.uk/radio/listen/live/r1.asx (high quality)
It is the direct link to the online stream, so you can paste this into an application like Winamp, VLC or whatever you use instead of having to keep a browser window open.
I am sure BBC don’t mind you using it like this but the url is buried in the html and is quite tricky to find (because of the frames) so hopefully this will save you some digging.
Thanks for all the comments and extra info
This also applies to BBC Radio 2, 3 and 4: