Note: A smaller verion of this demonstration, shown below, is available for use in classrooms outside the Broida lecture hall building.

A red, a green, and a blue bulb shining simultaneously on a screen produce white light. Since the bulbs are displaced from each other along the horizontal axis, placing an object in the light path blocks light from each bulb on a different region of the screen, and thus produces overlapping cyan, magenta and yellow shadows (which, where they overlap, leave shadows of the individual colors, red, green and blue, and, of course, black where all three overlap).

Why?

The human eye sees color by means of three types of cone cells in the retina. These cone cells have pigments whose absorption maxima are at approximately 560 nm (“red”), 530 nm (“green”) and 430 nm (“blue”). I have put these colors in quotes because while they give the relative positions of these absorption maxima within the visible spectrum, they do not necessarily correspond accurately to the colors that we would see for monochromatic light of those wavelengths. They also probably do not correspond to the colors we would see if only one kind of receptor were stimulated, each in turn. For light of a given wavelength or mixture of wavelengths, the color we see depends on the relative responses of the three types of cones. Any combination of lights that stimulates all three types of cone roughly equally appears white. If we shine a red light source, a green light source and a blue light source so that their beams overlap, the region where they overlap appears white. While the colored floodlights on the board in the photograph are not aimed at the same spot, the overlap of their beams is sufficient to illustrate the effect of mixing all three colors to obtain white. We can also observe the mixing of these lights two at a time, as shown in the photographs below.

Here, all three lights are shining on a screen. Facing the screen, the red lamp is on the left, green is in the middle and blue is on the right. We see that the center of the screen, where all three beams overlap, is white.
When we unscrew the red floodlight (ouch, hot!), leaving only the blue and green, we see, effectively, white minus red, which gives cyan (turquoise in some books).
When we remove the green light and leave red and blue, this gives white minus green, or magenta (purple in some books).
When we remove the blue light, leaving red and green, we get white minus blue, or yellow.
When you place your hand in front of the screen, for the reason noted above, it casts a set of three overlapping shadows, each one giving the colors shown above. In the photograph at right, we see clearly the yellow shadows where the blue light has been blocked, magenta shadows where green has been blocked, and cyan shadows where red has been blocked. Where pairs of these shadows overlap, they leave red, blue and green, and where they all overlap, of course, we see no color (black). This may be a bit clearer in the inset below:

The photograph below shows a smaller version of this demonstration.

This smaller unit has three colored laser pointers, one red, one green and one blue, aimed at a ping pong ball. To turn on one of the lasers, move the rectangular slider over the push-button switch. The photographs below show the unit in operation.

White (All lasers on)		Cyan (White minus red)		Magenta (White minus green)		Yellow (White minus blue)

References:

1) Hubel, David H. Eye, Brain, and Vision. (New York: Scientific American Library, 1988), pp. 162-169.
2) Rossotti, Hazel. Colour — Why the World Isn’t Grey. (Harmondsworth, Middlesex, England: Penguin Books, Ltd., 1983), p. 179.