The Gmail Manager Firefox add-on obviates the need to keep your Gmail open in a tab all the time by displaying your email info in a statusbar pop-up, as shown.

If you've got more than one Gmail account, the Gmail Manager can show you information from all of them, too. The extension is highly customizable - you can show unread message counts in all labels or just the Inbox, and in the case of multiple accounts, set it to automatically switch to the one with new mail.

Gmail Manager (Firefox)