I found myself annoyed by the Outlook Web App because one has to actually click on the OWA tab to see if you have any messages. With this extension, one can work in other tabs and know if they have any messages waiting for them or not.
This extension currently only works with the OWA URL format /owa/
Firefox Extension Page:
https://addons.mozilla.org/en-US/firefox/addon/outlook-web-app-show-unread/
Greasemonkey Script Page:
http://userscripts.org/scripts/show/171268
Chrome Extension Page (manifest file may need fixed):
https://chrome.google.com/webstore/detail/display-unread-count-in-t/eelenpkmbodgopefpbdghdmbeakcfnhc
https://github.com/pavanjared/OWA-Unread-Message-Count
Version 1.2.3 Update -Replaced custom title with unread count appended over Tinycon
Support the development of this extension via Bitcoin or Dogecoin (for transparency)! Bitcoin: 1DjZehKXGKAfecbcDYsjzT7pTmCXt5mFE1 Dogecoin: DPWbVMZespWTk9WVZQ8D5u25EPHvWiDrVn