At the time of this writing, Xbox Live is currently down. Turning on your Xbox 360 will give you a 'signed into Live' message, but then the system will idle for a bit (as seen above) and return to the sign in message. This of course follows Monday's background update meant to help prepare for the switchover to the New Xbox Experience in November, and the multitude of problems that followed. The US Xbox 360 support site currently lists Live status thusly:
Users will not be able to connect or log into Xbox LIVE. We are aware of the problem and working to resolve the issue. We apologise for any inconvenience this may cause.
Patience, my friends. I'm sure the issues will clear up soon enough. In the meantime I urge my friends to stop IMing me to complain that they cannot play Call of Duty 4 online.
Update: Larry Hryb, director of Xbox Live, tells me that the engineers have figured out what's wrong and are working on a solution.