Quick look on Google reveals a lot of different programs ranging from Free to $49 and up. Audacity is free but cumbersome for some to use.
Radiotracker searches for songs that you want that are playing on the internet, there is a small but growing backlash against radiotracker. Radio Vermont has started banning IP addresses for those using Radiotracker and other streaming programs. (Radio Vermont often plays the old classic William Cooper programs).
Replay radio is fairly simple to use and you can record to MP3, but a little pricey for some. But you can try it before you buy it (with limitations of course).