Streaming music

Is it possible to play audio streams in Unity 3D?

Yes you can:

http://unity3d.com/support/documentation/ScriptReference/MovieTexture.html

If no movie is needed, just leave it blank, you can still access the audioClip property.

Mobile phone solution:
http://unity3d.com/support/documentation/ScriptReference/iPhoneUtils.html

Yes, use the WWW class and the function:
function GetAudioClip (threeD : boolean, stream : boolean) : AudioClip
and specify the ‘stream’ parameter to true.

You can also put it on a single GameObject in an otherwise empty Scene then use Application.LoadLevelAdditiveAsync to stream it if this is for a WebPlayer build. I’ve used this method myself and it works fine.