I actually have something similar to this for my system, although I now use one as a Ubuntu desktop, and the other is a Ubuntu server - but it used to be Windows.
What I did was to hook the keyboard/mouse through a USB switch. For the video, I connected the dual-monitor system normally, using one monitor on the DVI output, and the other from the VGA output.
I then connected the Ubuntu server to the VGA output of the one monitor using DVI, and I use the monitor's video switch to switch between the two. So, it's possible to see one of the screens of the (formerly) Windows system (until the screensaver kicks in) while using the other monitor for Ubuntu.
Someone mentioned KVM switches. I've had a couple of these, and found them to be cumbersome and sometimes unreliable. I used them for ps2 keyboard/mouse, and when I moved to USB, instead of buying yet another one, I got a simple USB switch, and use the monitor switching for VGA/DVI. This gives a lot more flexibility (you can actually view one screen while typing on another, which can be useful if you are copying something from one to the other).
Also, decent KVM switches along with all the cables, isn't that cheap, and it's messy.