I have for a long time used Spotify on my cellphone, it's an app from a swedish company where you can listen to all kind of music just by streaming it on your phone and you can create offline lists too with music without being connected to any kind of internet.
I payed like 12 bucks per month for it but today when I was checking out the android market I found an amazing app called "Dood's music streamer
" and it's for free.
It's not as good as Spotify but it's an amazing app who's completely free with crazy much songs and you can create offline lists too so you don't have to be online to listen to your music on your cellphone.
Go and check it out!