they might be giants give out free mp3s to subscribers of their newsletters(and they don't give your email out to spambots), and their Dial-A-Song service lets you hear music, but not save it exactly.
but as far as general music downloading, its illegal without pay.
The singes are usually free for download off the artists' websites. If you want the other songs from the albums, there's no legal way to do it unless you purchase the album yourself.