The Burning Edge reports that the latest Mozilla Firefox nightly builds (2004-03-07) contain the Mail Integration UI newly checked-in by Ben Goodger (bug 214893). It adds a mail toolbar button that allows you to read your mail and newsgroups or send the current link to someone. A Ctrl-M shortcut key has also been added to allow quick access to composing a new e-mail.
See the mail toolbar button in action with the screenshot below.
The number of unread emails is retrieved from the registry (for the Windows version), the same key that allows Windows to display "You have X new messages" at the WinXP logon screen.
If you grab a nightly build, you have to go through a few steps to get it to appear. Go to the View menu -> Toolbars -> Customize. Drag and drop the Mail icon to any place you like on a toolbar.