A Polarizer Is Vital For Landscape Photography
I use a circular polarizer all the time when shooting outdoors. When outdoors, light is bouncing off all sorts of things, coming at your camera from a bunch of directions. The way I think of a polarizer is that it "aligns" the light as it enters the lens. The tangible benefits are cutting through glare and getting richer colors. And as a bonus, a typical polarizer adds ~2 stops to your exposure, so it doubles as an ND filter, too.
Here's two photos I took on a recent visit to Oneonta Gorge outside of Portland, Oregon. These two shots are taken moments apart. I have done no processing on either – the results are the default RAW processing of Nikon D7000 images done by Aperture.
Why such a difference? The use of a polarizer.
No Polarizer
Polarizer
On the left, I have the polarizer filter rotated so it's effectively doing nothing. See all the glare on the water's surface? And how the colors are washed out? This is not how I remember the gorge.
On the right, all I did was rotate the polarizer. Much better! The greens of the moss are richer, the glare on the water's surface is reduced revealing the stones beneath, and the overall scene is a touch warmer. A fringe benefit is the polarizer added about 0.7s to the exposure, smoothing the waterfall more. This is much closer to how I remember the gorge, and a much better starting point for post processing.
How do I know when the polarizer is positioned correctly? There's no one answer. It's scene-dependent. What I do is switch the Live View on my camera so the scene is visible on the LCD display. Then, rotate the polarizer until I like what I see. That's it. You can do the same thing when looking through the viewfinder – I just find the nice, big LCD display is easy enough to see.
For the gear heads among you, I predominantly use Tiffen filters. And I spend the money and get the good ones. A good circular polarizer will run you from $150 to $200, though it's money well spent. Don't cheap out on the filters. And the filters will last you a long time, probably longer than you'll have your current camera body if you care for them.