[mbq]

Honestly speaking, "colour" cameras we use every day are also false colour; they shoot 3 monochrome images in red, blue and green chunks of spectrum and mix the whole thing using plethora of parameters like white balance, or gamma. All this is heavily tuned towards human vision specifics to enable either monitor or print to induce a similar sensation in the viewer's brain that the photographed object would, despite the fact that the whole process retains only a negligible fraction of the information carried into the camera by the original photons. Quite a lot of animals perceive the hue of human-made photos and videos as totally odd, misexposed or desaturated, just because of having vision adapted to wavelengths or other properties of light which our processing mostly removes as redundant. Even more, one day humans may start to enrich their vision by technological or biological modifications, consequently beginning to perceive today photos as as dull as we see those old, monochrome ones.

[Sharlin]

To elaborate a bit, almost all digital cameras take a single monochrome exposure but each sensor element has either a red, green, or blue filter over it, in a mosaic pattern. From the relative brightnesses of neighboring pixels color data can be reconstructed and interpolated to form a human-viewable image.

[rodgerd]

The Foveon sensors are a sort-of exception to this rule, but they haven't really demonstrated enough visible benefits for them to become widely adopted.