I was shooting in Jedediah Redwoods State Park near the Oregon border and tried shooting the images below with, and without, a polarizer. As you can readily observe, there is a lot of reflection from the ferns and other foliage.
What's also quite interesting is that you don't need full sunlight for the effect to occur. Normally, the greatest polarization effect is 90 degrees from the direction of the sun (as this picture was shot). But in this case, the sky was completely overcast (the best time to photograph forests, by the way). The filter had a very great effect, as you can see! Do you also see that the colors are a deeper, truer, green?
Neither shot was adjusted...these are both straight out of the camera using auto-exposure and aperture priority mode...
Which would you rather hang on your wall?
Scene without polarizing filter.
Scene with polarizing filter.
When purchasing a polarizing filter, be sure to buy one that will fit your largest lens. You can always use reducing rings to fit to smaller diameter ones. You'll also want to be sure to select a circular polarizer, as these will work best for auto-focus cameras.
Be careful when using a polarizer on a wide-angle lens 16-35mm) - especially, the super-wide lenses (10-18mm), as the thicker lens may cause shadowing (vignetting) in the corners of your images. This is primarily an issue for full-frame cameras...not so much with the cameras using the smaller APS-C-sized imagers. The other issue with wide-angle lenses is that the polarizer may cause the tonal value of the sky to vary from left to right. This is why they are usually not recommended for this case. A similar issue presents itself when shooting a series of images to be used in a panoramic. As the angle of the filter changes in relation to the sun, the tonal value of the sky will change, making it near impossible for the panoramic software to fit the pieces together resulting in a consistent tone in the sky.