At various times, Outlook.com and Hotmail, Xbox Live, Skype, Office 365, and OneDrive had some problems. Microsoft has acknowledged the issue on the Skype Heartbeat blog, explaining that "we are now working hard to resolve a problem, where users cannot authenticate into Skype with their Microsoft accounts".
"We're investigating an issue in which some users may be unable to access or use Outlook.com services or feature", a notice on the Office 365 site said (here).
Microsoft has acknowledged the problems in an Xbox Live service status message, simply noting it's "working to resolve the issue as quickly as possible".
The Verge reports large numbers of users said they couldn't sign in to their Microsoft Accounts worldwide for more than an hour.
The service pages on Microsoft showed that by 10:30 a.m. Tuesday, OneDrive was back and running but there were still some issues with Outlook email services. "Thanks for your patience". "We'll provide an update shortly", said the service health page.
In terms of locations, the outages appear to be centred around the UK, Europe and the East coast of America. Skype seems to be hit in Japan and the United States east coast.