Google Calendar recently updated their favicon to a calendar page with a number on it, though the number doesn't change. With a simple user script, though, you can make it display the current date.
It's a small change, but pretty useful if you make use of, say, Google Chrome's app tabs. We've already mentioned ways to make favicons more useful for Gmail and Reader, and now Google Calendar's icon gets a bit more useful too (favicons, for those that don't know, are the small icons that appear next to a web page's address in the address bar — such as the "lh" next to Lifehacker's address). Just download the script and install it in your browser of choice (Firefox users will need the Greasemonkey extension to do so).