Personally my favorite way to download mp3 files is to use free web-browser addons, however, there are quite a few good desktop tools to get music in mp3 format the easy way like "GrooveDown" reviewed earlier.

sharkThief is yet another simple to use utility allowing music searching and downloading from grooveshark.com, featuring multiple stream download support the utility features advanced search, play, preview and batch download options to get things done fast at best speeds.