On Ubuntu, some people have had luck doing this using
Compiz Config Setting Manager. Run it and under
Accessibility category, you'll find
Color Filter and
Opacity, Brightness and Saturation filters. There you'll be get the desired effect with the available options. You can try options related to Grayscale or decrease saturation to zero to get the black and white screen effect. (I can't tell you the exact option since my current distro doesn't have Compiz Config support).
Alternatively, you could do the same by adding the following lines in your Xorg configuration:
Identifier "greyscale configuration"
Keep in mind that Xorg may not start with this configuration if your display drivers do not support such a low color depth value.