Microsoft has a Service Status web page that lists the current condition of Hotmail (re branded to Outlook in 2014). That web page also shows the statuses of Microsoft's other services, such as OneDrive and Messenger.
Unless the site is currently experiencing problems, Hotmail and Microsoft's other services are listed as running normally. A status history page is also available that records major service outages that affected a significant number of users. It describes the particular issues that users encountered, such as sign-in and syncing problems, and the dates when they were resolved. Microsoft also offers users a report page for problems not mentioned in the Service Status web page.