Microsoft has posted a notice on the Office 365 Service Health page acknowledging the login issues, calling them intermittent and "analyzing service logs":
Here's the text of the notice:
Title: Can't sign in to Outlook.com
User Impact: Users may be intermittently unable to sign in to the service.
More info: As the issue is intermittent in nature, users may be able to reload the page or make another attempt successfully.
Current status: We're analyzing system logs to determine the next troubleshooting steps.
Start time: Tuesday, March 21, 2017, at 5:15 PM UTC
Next update by: Tuesday, March 21, 2017, at 7:30 PM UTC
We'll keep you posted if and when things change.