I'm using 12.04 beta 2. I installed the classic desktop and I'm using the AWN dock. I tried right clicking on the bottom panel to delete it like you used to do in earlier versions, but nothing happens.
The secret key combination with the panels in Oneiric is Alt+Super + Right Click
The Super key is also known as the Win or Windows key.
If you are using Precise (12.04) then for me the same key combination is required.
However, as reported by @tachyons and @dobey the simpler Alt + Right Click is required.
N.B. if you are using Gnome-Classic (No Effects) OR for whatever reason compiz is not running then the key combination automatically defaults to Alt + Right Click
In fact - its the same key combination for any gnome-panel changes such as adding or moving panel applets.