Today in Stockholm, Steve Ballmer announced a collaboration with Spotify to bring their service to Windows on the desktop and on mobile. "Spotify will launch on Windows phone 6 and available for download on Windows Phone Marketplace. And yep, Spotify will be available on Windows Phone 7 where it has been designed from the ground up to take advantage of the design theme of Windows Phone."
As for Windows, Spotify already has a client app that takes advantage of Win7 functionality such as Jumplists and the ability to control music playing from the taskbar. And, Windows Live Messenger integration let you can share your playlists with your social network.