I spoke at the Sydney Adobe AIR Camp on Tuesday and for my session built an AIR app that I now think I'll turn into a complete application. It's currently for Mac only and runs on the Dock, it's icon only and when it launches you see a question mark overlayed on the envelope icon that I'm using. The app connects to your Gmail account and pulls back the quantity of unread mail, setting a new icon with an overlay of the quantity of unread messages.
Control or right clicking on the icon will show a menu listing the 10 most recent unread messages, all menu items will click through to their respective messages. I'd like to develop this further and add support for the system tray on Windows, but hey the original was only built over a weekend.
I've added an animated GIF below for you to see it in action, the red circle is only there to draw your attention to the icon, let me know what you think. I'll be releasing the source code for this some time next week.