A lot of people don’t realise there will be 2 very interesting features in Office 365 which makes connecting the dots with your on-premise environment and Windows Azure easy. The 2 features are directory sync and federation. It means you can use your AD account to access local apps in your on-premise environment; just like you always have. You can also use the same user account and login process to access Office 365 up in the cloud, and you could either use federation or a domain-joined application running in Azure to also use the same AD account and achieve single-sign-on.

Read more here:

http://blogs.msdn.com/b/plankytronixx/archive/2010/11/27/single-sign-on-between-on-premise-apps-windows-azure-apps-and-office-365-services.aspx