I'm a radio guy. Always was, always will be. Nowadays I listen to a few podcasts, but I love the "live" feeling of internet radio. I also love to sample shows, and luckily this can be accomplished by recording internet radio, as it streams. It's easier than you might think!
The first thing to consider is that many shows are already available as free downloadable mp3 podcasts. So if you're a fan of a certain station or show, be sure to check our their website.
Still, most internet radio listeners are more spontaneous, and if you're like me, you will constantly be coming across shows and think, "I'd love to be able to save this to listen to again later".
If you want to record a radio stations live stream to your PC hard drive, you could also try something like Radio2mp3, which is an easy to use, and pretty cheap little application for Windows. This is what I use, mainly for its simplicity. It lets you surf internet radio stations and start or stop recording at the click of a button. The MP3 is then yours to listen to whenever you want.
Mac users can use Audio Hijack, a massively popular audio ripper for OS X. I've used it on my Macbook, and it's a simply brilliant bit of kit, but remember that you have to start up Audio Hijack BEFORE the application you want to sample. This could mean losing information in Safari tabs for example, so be careful!
Wether you're a Windows or Mac user, you can edit, trim, and export your audio files with hugely popular cross-platform software Audacity It's free too!
Good luck with your radio ripping.