Sometimes you can capture the stream directly. With one site, all I have to do is open the page in IE, then click on properties in the Windows Media player box. Find the address and save it to the clipboard. Open that address in Firefox, which then opens Winamp on the stream. Find the stream address in Winamp, copy that to the clipboard. Finally, use a command-line player called mplayer like so:
mplayer -dumpstream "the address from Winamp" -dumpfile filename.wma
Mplayer receives the stream and saves it to filename.wma
Nothing to it. :)