Think of it this way, why do we wear polarized sunglasses? To cut glare.... Think of a circular polarizer as sunglasses for your camera. I probably use my Singh-Ray polarizer for 75 percent of my shots. For a landscape photographer, it is one of the most useful tools available and the effect can not be reproduced in post processing.
One of the best uses of a CPL (circular polarizer) is around water and forest scenes. The polarizer will cut the glare from the water surface as well as from the wet rocks. Let's say we are shooting a forest stream, we are most likely going to find rocks, trees, shrubs and bushes. All of these surfaces are affected by light and can have some color robbing glare, even on dark cloudy days.
Here is an example of a scene shot without a polarized effect and with polarization. Notice not just the water, but the leaves, ferns and trees also have reduced glare and enhanced color. The scene was shot using a 16mm extreme wide angle lens by the way.