Seems like Google Music finally went out of beta today and it remains a free service which allows you to store up to 20,000 songs in your personal music library (Terms of Service).
The release also comes with a number of new features and a New Music Store on Android Market that works seamlessly with Google Music. The store has hundreds of free songs as well as millions of tracks available for purchase via the web or Android device. The purchases do not count towards the 20k song limit.
As far as social integration, it allows you to share a free full play of any purchase with your friends on Google+.
Even though I am a loyal iTunes user and do purchase 99% of my music thru there (yes there is that 1% that I've bargained shop at Amazon), I do like options and I think it is great that they finally made their full release of their own music service. In the end I really love and pay (testing as dev now) for iTunes Matching since most of my library was purchased on iTunes + I love how it integrates with all my iOS devices. I do have most of my music on the Google Library as well because I let their handy uploader do it all for me but it did take a couple of days to finish.
Anyways, glad it is out and for all you apple haters, there you go another option.
All hail Steve :-).