Xbox Live has gone down. Life as we know it is at an end. Microsoft is aware of the issue with the online service and has apologised to gamers having trouble logging in.
A message on the XBL status page says
"users may experience difficulties signing into Xbox Live from an Xbox console" and "signing into Xbox Live from Xbox.com. 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"
Xbox Support Twitter account also says:
"We are aware of the issues some users are having with Xbox Live and are actively investigating. Thanks for your patience."