Check the websites of your favorite bands to see if they have free downloads. You can often get one or two free songs. Some artists, like Radiohead and Girl Talk, have had a system where you can get an entire album and pay any amount you want. You don't have to pay anything; but in the case of Girl Talk, you do get a message asking why you don't want to support music and it can make you feel guilty.
Look at general media websites. Like your favorite bands' sites, your favorite magazines might offer free song downloads or their own compilation albums. The sites of television networks can have some free downloads or even full albums of music featured on their programming. Record labels' sites can offer free music from their artists too.
There are a number of legal free music sites that offer full album downloads. Ten of them are provided in the link below, but a search engine can obviously be of use as well.
Now burn away.