Minimize to system tray (Thunderbird)
From MozillaZine Knowledge Base
Thunderbird cannot minimize itself to the system tray. However, users of Microsoft Windows can try using Thunderbird-Tray, ThunderCalTray, or one of the utilities mentioned in this thread for minimizing Thunderbird to the tray.
If you use GNOME, you can (like with any mail program, or even without one) add the Inbox Monitor applet to your panel, and configure it to launch Thunderbird upon double-click; however, each monitor can only watch one email account.