Streaming music over the Internet has always been a legal gray area. Most streaming music sites tend to call themselves radio stations but the music industry thinks of them as independent media consumers and that is the reason that while radio stations get bulk deals for playing content, online streaming stations have to pay for each song streamed on a per user basis.
This, as you can imagine, doesn’t really bode well for sites that rely solely on advertising to cover their costs as advertising spots for all but the biggest sites are usually pretty low.
A lot of streaming sites have gone under trying to perfect a monetization strategy for online music and only a few have managed to survive. Among them Pandora is the most famous and while it is one of the few sites making any money, it is only accessible to people living the United States.
For people outside the US, Grooveshark is an excellent alternative to Pandora.