The Xbox LIVE service is currently down, according to Microsoft's own server status page. The status for Xbox LIVE states that users "may experience difficulties" signing into Xbox LIVE on their Xbox or through the xbox.com website. Microsoft is working on a fix, though. From the server status page:
We are aware of the problem and are working to resolve the issue. We apologize for any inconvenience this may cause and thank you for your patience
The cause of the Xbox LIVE service disruption is unknown, and Microsoft has not issued an official statement yet. This is the same LIVE service that is set to be rolled into Windows 8 with its release, though some gamers have concerns that it could mean difficulties for indie developers.
Note that Xbox LIVE is the only service that is currently down. The Xbox LIVE marketplace is still up, as well as the matchmaking service. No apps seem to be affected either, and the Zune service is still active, though that will probably be renamed soon, as the Zune brand is quickly being put out of its misery.
Updates will follow if service resumes, or if further information from Microsoft is forthcoming.