Based on what I have read, a polarizer is a “must have” filter when near water or when the sky is blue and filled with puffy clouds. Or, at least that has been my “take away” when reading various articles by the experts. Near water and other reflective surfaces (automobiles and foliage, for example) the polarizer cuts the reflections. And when it comes to blue sky and clouds, the filter can brighten the blue and keep details in the white clouds.
In the two examples below, the polarizer was able to simplify the composition in photo #1 but cutting out the reflections being created by the surrounding vegetation.
But just because you have a polarizer in the camera bag doesn’t mean it must be used! I actually find them to be cumbersome to use, as the more times you screw one on and screw one off, the more likely it is that you will drop it or at the very least smudge it or the lens. In the situation below it would mean potentially dropping the polarizer in the water, so I didn’t bother with it in photo #2.
These two images are very different. I don’t know which I like better, but my current favorite is photo #2. That’s because it seems kind of artsy and abstract. I guess any time a photo makes me feel like an actual artist, I like it. YMMV.
Photo #1: With Polarizer
Photo #2: Without Polarizer