If you remove the menu from the panel and hit Alt + F1 the menu will appear at the mouse cursor. If you use Compiz you can then use the commands plugin along with xte to simulate keyboard presses and make Alt + F1 be any mouse/corner press you want.
xte is part of the xautomation package: sudo apt-get install xautomation
This is a helpful tutorial on the Ubuntu Forums.
There is also MyGTKmenu, which allows you to easily create your own custom menu.
Then there's apwal, which allows you to create a custom application-launcher-thing (something like an "application wall", get it?) which can be assigned to open with mouse buttons. It's available in the repos.
Then don't forget about GNOME Do and Kupfer, which in my opinion are far superior to any menu.
Oh, and don't forget about the mouse gesture program Easystroke, which allows you to run any keyboard command, script etc., with simple mouse movements rather than having to click your desktop at all. For example, I can open my main menu by holding the middle mouse button and moving the mouse up. Takes less than a second and it doesn't matter what window the pointer is in. It's available in the repositories.