The official notice:

Dear Xbox LIVE Members:

During this past holiday season you helped us break a number of Xbox LIVE records. This included our largest sign-up of new members to Xbox LIVE in our 5 year history and just yesterday you broke the record for the single biggest day of concurrent members ever on the service.

As a result of this massive increase in usage we know that some of you experienced intermittent Xbox LIVE issues over the holiday break. While the service was not completely offline at any given time, we are disappointed in our performance. I would like to take this moment to thank each and every one of you for your patience and understanding as our team has worked around the clock to return the service to a stable state.

At the same time we would like to offer a token of our appreciation to all of you in celebration of record success for the service. And as a thank you for your loyalty during this holiday period, we will be offering all of our Xbox LIVE members around the world access to a full Xbox LIVE Arcade game that will be available to download free of charge. In the coming weeks we will be sharing the specific details of this offer with you.
Thank you again for helping make Xbox LIVE everything that it is today!

Sincerely,

Marc Whitten
General Manager, Xbox LIVE