www.rdio.com
$5 a month and I have unlimited access to all the music I want.* I haven't illegally downloaded any music since I signed up several months ago. Can't speak highly enough of it. I'm sure the other streaming music services out there are the same.
However I don't really see how much money gets back to the artists. A typically album costs $10, I pay half that and listen to dozens of albums a month. I suppose it's better than nothing.
*Well almost. They don't have everything. But their selection is massive.