YouTube - The favicon changes based on whether the video is buffering, playing, or paused.
Gmail - Incompatible versions of Internet Explorer show a damaged envelope as the favicon.
/via Eric Hansz
Colllor - The favicon changes to match the chosen color
Flickr - The favicon turns into a live indicator showing the progress of the upload.
Chrome - Accent colour on most visited thumbnails is pulled from the site’s favicon.
/via Andrew Procter
Google Calendar - Favicon displays the day of the month.
Campaign Monitor - The favicon shows a closed email when logged out, and changes to an open one when logged in.