Over the past couple of days, users of Microsoft's Hotmail and Outlook.com mail services have been unable to access their mail, thanks to what appears to be an issue with Exchange ActiveSync. iPhone, iPad and Android users, including some Windows Phone and Surface RT users, have been affected by the issue, which Microsoft still hasn't fixed despite many posts on the Microsoft Answers forum starting several days ago.
The issue doesn't affect those accessing Hotmail or Outlook.com via the web, or via POP-based accounts, a Microsoft moderator posted on the Answers forum. A statement from Microsoft to ZDNet doesn't reveal much more info, but it seems like they are looking into the issue.
Microsoft is investigating an issue affecting a small percentage of mobile users' access to Hotmail and Outlook.com, and we are working to restore full access to the service as quickly as possible. For the latest information, we encourage users to visit the Hotmail and Outlook.com status page.
One associated issue appears to be that Microsoft's status pages aren't showing an issue, so users are becoming frustrated as to why mail on their devices isn't working. Unfortunately anyone affected by the issue will have to simply wait it out while Microsoft sorts out whatever is wrong with Exchange ActiveSync.
Update: We're also hearing (thanks to those in the comments) that people are unable to sign into Skype using their Microsoft Accounts. We've contacted Microsoft to see if the two issues are related.
Update 2: The issue relating to mobile access of Hotmail and Outlook.com has been resolved several hours ago. When it comes to the Skype/Microsoft Account sign-in issue, this is unrelated to the mobile EAS issue; the Skype team is "aware and investigating the issue". More updates can be found on the Skype blog.