1)One of the other posters here tells of using a small FM transmitter connected to his computer audio jack to send what he listens to on the 'net to his FM radios, etc. I do the same. He suggests an FM unit from the C. Crane company. I use another brand but the effect is great if you don't want to be tied to your computer to listen.
2)There are two software products that I've found that will let you record internet radio to an mp3 or WAV file, and you can set up a recording schedule that will automatically record the programs you want as long as your computer is left on and connected to the 'net. The most expensive one is called "Replay A/V" made by Applian Technologies. A less expensive software is by the company pdmarq.com and looks similar to Replay A/V but I've not used this product. I use Replay AV. If you intend to use these softwares, you have to know the URL of the audio stream to insert it into the recording schedule. Both of these products are PC only. The recording schedule you set up is time-serial only---that is, you cannot record programs that are broadcast at the same time. Note: there may be other software products that record audio but I have not found any that will let you set up a recording schedule other than these two.
3)For public radio people, the web site
http://www.publicradiofan.com lists all public radios and will give their audio URLs as well as a list of stations that carry a given program at various times during the day. So, for example, you can look up Democracy Now and see a list of all the stations that carry it at various times, with their audio URLs. The site also shows radio stations world wide with their audio URLs. This is a U.S. located, privately maintained site.
Hope some of this info is useful to 'net listeners.