The indicator-applet in Gnome was added with Ubuntu 10.04 to notify the user about incoming messages.
The default indicator applet works with Evolution and Empathy (which replaced pidgin a while back as the default IM application)
With the Thunderbird addon Thunderbird Indicator, you can add the notification for Mozillas Thunderbird as well.
quote from https://launchpad.net/libnotify-mozilla/
This is an add-on for Mozilla Thunderbird which notifies you of new mail messages via Ubuntu’s standard notification system and the Messaging menu. Once a new mail is received, the Messaging menu’s icon turns green and a notification pops up. The Indicator Applet also provides quick access to your contacts and allows you to compose a new message.
Simply add the repository using
sudo add-apt-repository ppa:ruben-verweij/thunderbird-indicator
and install via
sudo apt-get update && sudo apt-get install xul-ext-indicator
The detailed installation instructions can be found on the ubuntublogger blog