There are lots of streaming internet radio stations around the world that you can listen to online for free. There's also a handful of good player apps for Windows, to make it easy to search for stations that might be of interest.
But here's an absolutely wonderful program that takes your web radio listening to a whole new level. The program in question is called Streamwriter, and it's available from www.streamwriter.org.
First, Streamwriter is a pretty good internet radio player with an inbuilt, categorised list of stations. So whether you want Celtic, rock, classical or anything else, just pick from the list and start downloading.
Second, Streamwriter can record what you're listening to, straight to an MP3 file. Actually, if you want to, you can record up to 10 stations at once.
Finally, Streamwriter has a programmable search facility that's absolutely amazing. Want to download lots of Beatles tracks? Fancy a copy of Roy Orbison's Pretty Woman? Just type a search phrase into the Wish List box, then leave the program to do the rest. It'll keep a constant eye on all the stations it knows about, and record the songs if/when they come up.
Streamwriter is a 4 MB download, and should run on Windows XP and above. I've checked it with VirusTotal and it appears clean. There's a portable version available too, if you want to try it without needing to permanently install it.
My thanks to Panzer for alerting me to this great program.