There are two ways to desaturate an image:
Here is a sample photograph converted using this method.
At first glance there seems to be little difference between this method and the straight grayscale conversion or gradient map conversion.
However a look at the color chart shows just how different the two methods are:
All colors are converted to middle gray. The difference is more apparent in a photograph with low contrast. Notice the difference in the windows.
Desaturation by itself gives very poor results. However, desaturation forms the basis for the Hue-Dialing method, which produces even better results for low contrast photographs.
For more comparisons check out the Comparison Page.