Many people use polarizers to darken blue skies and make white clouds pop. When the sky gets covered by heavy clouds, the polarizer stays home, or in the photo bag. While the polarizing filter is not of much use for the overcast sky itself it can still help with what lies below.
The colorful fall foliage is the prime candidate! Overcast rainy days are actually great for capturing the wild natural colors. That is as long as you can eliminate all of the glare from the diffused light bounding all over. And that is where a polarizer can be invaluable.
In this first photo, no polarizer was used for the close up of some colorful maple leaves in the rain. Yes, some color is there and it stands out well from the green leaves behind, however, there is a very easy way to get so much more out of a scene like this.
Just look at the second photo. The only difference is that a polarizer was in place and rotated for maximum polarization, all else remained unchanged. And you can see that not only did the foreground yellow and orange colors come to life, so did the background green leaves, previously obliterated by glare.
Many things can be tweaked and improved in post-production but this sure is not one of them. Once the color and detail are gone they are gone. Plus, it takes 1 minute in the field and it's all set, no need to sit behind the computer. Instead, you can be out there enjoying the outdoors and capturing more photos.
For a full disclosure, these photos are almost straight out of the camera to show the polarized effect without interference from post-processing. I have only scaled them down and applied sharpening, absolutely no changes to exposure or colors.
In the second pair of photos, the same difference. The first photo without a polarizer has glare not only on the leaves top right but also on the gravel on the path. You can see a dramatic difference in color between the two.
This one is more interesting though in my opinion. While the foliage clearly wins in the second polarized version, I think the gravel path is a whole different story. That one, I think, depends on one's taste and what the photo tried to communicate.
Whats the moral of the second comparison? While polarizers generally help, sometimes, they may not be the right tool. If it is the glare that caught your attention in the first place, polarizer is not what you want mounted on your lens.
Just search for "circular polarizer 72 mm" and replace the 72 with the size of your filter threads. I have had a very good experience with Hoya filters, including their polarizing filter.
Circular polarizing filters usually absorb about 2 - 2.5 stops of light. So white they help with eliminating glare and saturating colors they will slow down your shutter or demand higher ISO. Some people like them for that since they can serve a double duty as a polarizer and a neutral density filter in one. Very handy for flowing water or waterfalls.
If that is not what you are after though, especially if shooting moving subjects you want in clear focus, the Hoya HRT circular polarizer may be the right choice since is passes a notch more light through (about 1/3 of a stop)
Have fun with the colorful season!