I have just tried to open my Outlook.com account and got an error message, tried Hotmail and it has the Same problem. According to Microsoft service status dashboard
We’re having a problem accessing email. You might not be able to see all your email messages. We’re working to restore service right now. Fixing the problem is taking longer than we hoped. We’ll provide an update by Mar 13 2:12 PM. We apologize for the lengthy interruption in service.
Last month we reported that Microsoft will begin moving customers to Outlook.com from its Hotmail service. It might be an issue related to that but we aren’t sure about it. Hotmail/Outlook users are heading to Twitter for reporting their error status, Many said they were unable to check their mail and some asked friends to use alternative methods to reach them.
According to Microsoft spokesperson, Company is investigating an issue affecting a small number of customers’ access to Hotmail and Outlook.com, and we are working to restore full access to the service as quickly as possible. For the latest information, we encourage people to visit the Hotmail and Outlook.com status page (https://status.live.com/)
