Here is the latest status update from Microsoft:
Current Status: The investigation determined that a portion of infrastructure which facilitates authentication to the service is experiencing higher-than-normal resource usage. Engineers are analyzing service telemetry to determine what is causing the high resource usage.
User Experience: Affected users are unable to connect to the Exchange Online service when using multiple protocols including Outlook, Outlook Web App (OWA), Exchange ActiveSync (EAS), and Exchange Web Services (EWS).
Customer Impact: A higher than average number of customers are reporting this issue. Analysis indicates that customers will likely have some users experiencing this issue.
Incident Start Time: Wednesday, July 15, 2015, at 9:25 PM UTC