This is probably what everyone one wants these days.
Last.fm:This thing has a Free Music Downloads section in bottom of the page, One can go there and browse for free downloads in that section, Of course the Downloads are limited still one can listen to unlimited and new songs there. I use this site frequently to share the name of my favorite tracks in my Twitter and Facebook.
ARTISTdirect:This is a brilliant place for free music, Some of the big releases aren’t always free, You need to pay for them. Still I use it a lot to see new tracks by top artists. One can use this site for browsing music by various Artists.
Kazaa: This site can be used to listen and download lots of free and latest music but this is only open for US. Not for any other country.