In 12.04 with a two monitor setup (using unity and compiz), is it possible to switch workspaces individually for each monitor?
I spent considerable time trying to find a solution for this. My conclusion is that while compiz once had support for this, it has not been functional in a while. Since Unity uses compiz, it cannot do it either at the moment.
There seem to be very few window managers that support this feature at all. The only one I was able to find was xmonad, which is a keyboard-driven tiling window manager intended for power users willing to spend quite a bit of time learning how to use it. I think I've seen references to awesome being able to do this too, which is another similar tiling window manager.
So unfortunately the answer for compiz and unity seems to be "no, not possible", and the answer more generally seems to be "no, not unless you are willing to switch to a tiling window manager".
I know this is old, but for people looking into this, Enlightenment 0.19.x (http://enlightenment.org) has good support for multiple screens, and is able to switch workspaces independently or simultaneously on two screens (haven't tried with three or more). I switched from xfce4 and haven't looked back. You can find a PPA at https://launchpad.net/~niko2040/+archive/ubuntu/e19
EDIT: The reason this isn't common functionality is that it violates a freedesktop.org specification (EWMH - http://standards.freedesktop.org/wm-spec/wm-spec-latest.html) that most window managers follow. Those window managers that support this simply do not follow the specification.
Actually, you don't need to use a tiling window manager. As far as I know, xmonad and awesome support this feature, and i3 does to a certain extent.
But they are all tiling. Wingo is a hybrid window manager that has per-monitor workspaces, and it can be used as either a regular window manager or a tiling manager (or both). Note that it is self-described as "very alpha".