By default, the favicon for Gmail is the boring old Gmail logo: . There is a way to update that icon, and have the favicon reflect the number of unread emails in your Gmail inbox.
To do this, you will need to go to the settings in Gmail by clicking on the gear icon, , and then select the Labs list of settings:
Find the Unread message icon lab:
Click Enable, and then save changes. Now your tab will always show you how many unread messages you have in your inbox.