Rhapsody is such a site, as is Napster. In order to download as much as you want to an mp3 player you'll need to pay for the "to go" version, which will allow you to put songs on supported players. To use either you will also need to download the software and have a player that supports subscription music. You'll need to go to their sites to find out what players each supports. Once you sign into the software, connect the player and then you'll need to authorize it. Once you do that, then you can d/l as many songs as you want. You'll need to connect the player to the software at least once a month to renew the license to play the songs you downloaded. Once you stop paying the stop being playable once your subscription expires.
Rhapsody and Napster do offer a few free downloads. I think Rhapsody does a free song of the day. That's about the extent of free.
I am not very computer literate...so need help I signed up for Rhapsody..because I had read it was free downloads...I want to be able to go to a site, download a song to my MP3 Player, either free or by a subscrption where you get as many downloads as you want per month. Is there such a site.