As reported Xbox Live had severe issues during the holidays for many Xbox 360 users. Even today there are still issues, specifically: Xbox 360 and Zune account creation, renewal, recovery, and logging into or creating Windows Live ID accounts can be labeled as not working.

In a statement posted on Xbox Live spokes blogger Major Nelson a statement of Marc Whitten, General Manager of Xbox Live blames the issues onto the huge success of Xbox 360 sales.
There is always a way to spin issues into the positive. In any case all Xbox LIVE members will get a full Xbox LIVE Arcade game that will be available to download free of charge. Details will be revealed in the coming weeks.
Via the Major Nelson site.