Mac only - Danny Orog from APC magazine describes Rogue Amoeba's latest release, Radioshift, as 'tivo for internet radio'. It lets you capture internet streaming (or regular radio) on your mac, for later playback. You can search from over 50,000 listings of internet radio stations, and filter by genre or geography.
Looks like there's a catch or two though, first up it's paid software ($32) and if I read the article correctly, you need a $US50 radio appliance (Griffin's Radio Shark) to use it. I've contact Rogue Amoeba who make the software to find out about getting a review copy, and hopefully I'll be able to clarify whether you can use it with any internet radio receiver. I'll keep you posted!