With Thunderbird 2.0.x it was possible to integrate with Ubuntus notification system.
The Libnotify plugin intents to improve the integration with libnotify. With this plugin, Firefox and Thunderbird will display notification message like "new mail received", "download complete" using the libnotify library. For now, only Thunderbird displays notifications, but it stopped working with release 3.x
The latest beta release solves the problems and works with TB 3 like a charm.
Download the extension from here and install it from inside Thunderbird.
You can also have a look at the list of beta releases, in case a newer one is available after having written this post.