Icetray

Features

for all applications:
show/hide a single or all windows
restore windows to their previous state, position, size
restore each window to its original virtual desktop/workspace
activate restored windows
hide to tray on close
hide to tray on minimize
start minimized to tray
show icon only when hidden to tray
mouse scroll on tray icon shows/hides
GTK-themable icons
StatusNotifierItem support (can be disabled by with_appindicator hidden pref)
customizable tray icons
popup menu (show/hide individual windows, open new windows, quit)
command-line -icetrayShowHide option (useful for window manager's keyboard shortcuts)
command-line -icetrayPresent option (activates windows)
middle click on the tray icon activates last registered window
for mail applications:
display unread message count in tray icon
display biff in tray icon for new messages
include/exclude mail accounts to/from messages count
include/exclude folders types to/from messages count
count in sub-folders recursively
handle Exquilla accounts
restrict message count to favorite folders
trigger external program on message count change
show icon only when new mail (mutually exclusive with show icon only when hidden to tray)
for applications embedding chat (currently only Icedove-UXP)
display additional system tray status icon

Under Linux:
GTK+ 2.20+ required.
libappindicator3 can be used for StatusNotifierItem (KDE, Unity).
Under Windows, few features are not yet implemented.
Icetray temporarily unsets:
the tabs.warnOnClose built-in preference, which otherwise disrupts the handeling of the close event
mail.biff.show_tray_icon for mail applications

windows aren't restored with the same z-order, but there is no means to correct that under Linux
notifications for excluded mail account servers are not disabled. Newmailalerts are hard-coded and we can't easily disable them on a per-server basis (only globally, see mail.biff.show_alert). The proper way would probably be to disable default notifications globally, and handle notifications ourselves. This is out of the scope of this addon, but you may want to give a try to the MailAlert extension
child windows (compose message, preferences, ...) are not handled by Icetray. For ex., they are not hidden along with there top-level window.
because of getNumNewMessages()'s strange behaviour, it's impossible to display an accurate count of new messages. The best we can do is display a biff icon.
POP users should set http://kb.mozillazine.org/Thunderbird_:_FAQs_:_Automatically_Download_Messages to see new message. See this discussion.
some features do not work well under Unity/Compiz.