A while back when I first converted my little netbook to Ubuntu Linux, I wasn't sure I could get it working but I installed some Spotify beta software and to my surprise it did work. I find Spotify quite a good service, although I don't subscribe to it as I don't quite have the listening time to make it worthwhile. The adverts are a little bit annoying but are bearable. I particularly like the top lists, where I've come across up-to-the-minute music that I've liked for six months or more before they form part of my wife's consciousness - she's very conservative when it comes to music.
There are no shortages of internet radio stations or music services but if you are interested in discovering new music, I'd recommend Spotify. The free version includes adverts and there is a limit to how much per month you can listen to but I've never hit that limit. As I write the limit is 10 hours per month, which is 2.5 hours a week, easily within my limits.