DeviantArt user Vhanla has created a Google Music desktop application which lets the users to access and control music stored in Google’s cloud using multimedia keyboard, taskbar buttons or sidebar widget on desktop.

Features of the Google Music Desktop Player
A notification splashform
LastFM Scrobbling
Frees RAM after song end
Uses Webkit Engine
Supports Multimedia Keys [Play/Pause, Stop, Previous and Next]
Windows 7 Taskbar support [Buttons for: Play/Pause Previous and Next]
MiniPlayer
Metro UI Like with Aero Snap support
You can download Google Music Desktop Player For Windows for Windows desktop.
Download Google Music Desktop Player