Edit: We ask that you please do not create more threads to report this issue. :)
Update 3:10pm PDT - I see a few asking about Error 37. That error occurs when the realms are unavailable. As we're working on this issue still, you may see Error 37. As before, we do not need further reports of this. We will do what we can to get the authentication server back up and working properly as soon as possible.
Update 3:54pm PDT - We're still investigating the cause of these issues and have brought all Diablo III game servers offline for maintenance. We will provide updates as they become available.