Nowadays, there are indeed many sources to get mp3 downloads from. They're not all the same, however.
These sites providing mp3 music differ on many things, such as the size of their mp3 collections, the particular mp3 songs available - many of these sites won't have the most popular releases or they'll come at a price -, the existence of a "premium membership" in order to have access to certain mp3 downloads, etc. Some players will even profit from their current place in this uprising market to impose their own conditions.
With all this being taken into account, one place I've lately found to be a refreshing surprise is Amazon.com. They have quite a big collections of mp3 songs to download and you can even upload your own mp3 music, so the availability of new songs to download is ever growing. Sure, if you want your mp3 player to have the latest, most popular hits, they will come at a price, but they're usually not too high.
So, good luck and enjoy your free mp3 downloads !