GIMP

GIMP has several methods to reduce the colors of a digital image into shades of white, gray and black.

Very simple: Image/Mode/Grayscale.

The Desaturation Plug-in desaturates three different ways.

Desaturated on Lightness.

Desaturated on Luminosity.

Desaturated on Average.

The Decompose Plug-in is available at Colors/Components/Decompose.

Original, red, green and blue. (RGB)

Original, hue, value, saturation. (HSV)

Lightness, a and b. (Lab)

Luminosity, blueness and redness. (YCbCr)