Look for independent bands. The often will offer totally free music downloads on their web sites. Often even commercial bands will offer the same thing for a limited amount of time as a promotional event. On occasion you will be asked to join the bands fan club in order to initiate the download.
MySpace is a great place to get totally free music downloads because there is such a huge following in the music community there. Even big name artists have pages with music on them. Most of the music is only available to listen to, however sometimes the indi bands and even the big names will offer a song or two as totally free music downloads.
There are paid membership mp3 services were you pay a certain amount per month for up to a certain amount of downloads. Often these sites will offer a daily free download for members of the service.
Look for sign-up bonuses when you sign up for an online music service. Many of them will give you a certain amount of free downloads when you sign up and purchase other songs.
Look for digital downloads when you buy a CD. This is becoming very common with movies already. Digital downloads are totally free music downloads which don't cost anything for the purchaser of the disc.