We've seen outages of varying lengths before, but it looks like Hotmail is experiencing some pretty major issues right now, with the service showing an error upon login for most users.
The hotmail status page is reporting "hotmail is having sign-in problems right now, you may see an error message," however, it doesn't explain when the issues will end or what the error is. To get around it you can click the Hotmail icon in the top navigation bar, which is working for some users.
Update: It looks like it's back! No explanation why yet, but Hotmail users can rejoice!