After the planned downtime on Monday, Xbox LIVE is having issues with periodic outages.
The official Xbox.com Support page states that Microsoft is aware of the problem, announcing "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 apologize for any inconvenience this may cause."
XBL also experienced some unexpected downtime on Tuesday. There's still no word on how long the service will be down.
Update: As of this afternoon, Xbox LIVE is up and running.