This is harder than it used to be, because of the removal of Compiz Config Settings Manager (ccsm). So far, I have managed to not re-install ccsm on my Ubuntu 12.04 Precise Pangolin system, trying to do it the “Ubuntu Unity Way”, but this was the deal-breaker that forced me to re-install it. I need this keyboard shortcut, as it is fundamental to my day-to-day workflow—I don’t know how this is not a first-class keyboard shortcut! After installed, go into ccsm, and scroll down to Window Management / Put. Check Put (activate it), then click into it. Enable “Put to Next Output” for the keyboard (not the mouse), then tell it to grab your keyboard combination. I use Ctrl+Alt+Spacebar, which it translates into <Control><Primary><Alt>space. Once done, press Ctrl+Alt+Space and marvel.
There's not much in this for me besides recognition.