1: There is an extension that integrates Thunderbird with the Ubuntu Messaging menu (and also provides NotifyOSD notifications) that comes in a PPA. Here's a screenshot:
To install it in Ubuntu, use the following commands:
sudo add-apt-repository ppa:ruben-verweij/thunderbird-indicator
sudo apt-get update
sudo apt-get install xul-ext-indicator libnotify-bin
You'll then find it in the Thunderbird extensions. The PPA provides packages for Ubuntu 10.10 and 11.04, though the 11.04 version is a bit more advanced and allows you only display notifications for messages that arrive in a certain folder, etc.
2: There is also an extensions you can directly install in Thunderbird, based on the above extension, however I've only tested the extension above. You can get it from Mozilla Addons site.