Office 365 will no longer support Internet Explorer 8 after 8th April 2014. 

For the best, richest experience with Office 365, we strongly recommend that you upgrade to the latest version of Internet Explorer. Internet Explorer 10 is available now, and Internet Explorer 11 is coming soon. Modern versions of Internet Explorer offer faster web browsing, integrated spell-checking, improved security, and more.

Internet Explorer 8 users will not be blocked from connecting to Office 365 after 8th April 2014; however, Internet Explorer 8 users should expect slower performance with Office 365’s Outlook Web App and other Office Web Apps. 

If you experience a technical problem connecting to Office 365 from Internet Explorer 8 after 8th April 2014, Microsoft Customer Support and Service may need you to reproduce the problem on a supported browser.