There remain some slightly confusing statements in this thread. The video to which smoke665 offers a very good description of how a polarizer works, where it can be useful, and when it may cause problems. The example of the water where reflections of the trees are eliminated by the polarizer is a situation where the photographer's taste comes into play. If you really want to capture detail below the surface of the water, then, the polarizer is your friend. If the reflection of the trees is an important part of your creative intent, then you would want to minimize the polarizer's effect.
I believe we should also keep in mind that a polarizer will have an effect on light, no matter its source. If you are shooting indoors at an aquarium, for example, a polarizer can be very useful when shooting through aquarium glass. The trade off, of course, is that, used at its maximum effectiveness, a polarizing filter robs you of at least a stop, often more than a stop of light. Many aquaria are dimly lit, and their inhabitants are in constant motion. This is another of the inversely proportional choices by which we photographers are challenged. I, personally, have experienced great success and great failure in capturing aquarium shots using both approaches. Higher ISO helps to compensate for the loss of light, and also helps to "freeze" motion, but results in greater noise. A larger aperture helps with light, but reduces depth of field. I love photography.
Back to polarizers, they can be helpful when shooting subjects wearing glasses to reduce those photo-ruining reflections that obliterate the subject's eyes, whether indoors under artificial light, or outdoors in sunshine. On the other hand, a poloarizer might also eliminate coveted catchlights (pleasing reflections) in the subjects eyes (I love photography!).
This has been an informative discussion. I am glad I came across this thread.
Caruso