There are a few items that you should have with you at all times. A circular polarizer definitely falls into that category. It does not use up much space and can be used for a lot of “effects” that can hardly be imitated if at all.
Giving more contrast to the picture in certain situations, especially landscape scenes, is just one of the reasons to own one, another application is the removal of reflections on non-metallic objects like a pond or window when aligned in the proper angle.
A knock-on effect is the decrease of light by 1 to 3 stops based on the quality/brand, but in a way this can also be used as a benefit depending on what you want to achieve (a dedicated ND filter is still better of course).
What you should keep in mind though is that by using a filter you are adding extra glass, don’t buy a 40€/$ filter for your L lens – that would be like putting winter tires on your sports car, it works, you are just not making the best out of it. But don’t be afraid to get one of these when you are starting, it’s still better than none at all. I personally went for the high end versions due to my L lenses: B+W Käsemann MRC, which will cost you about 120€ for the 72/77mm versions each. I can clearly see the difference between my cheaper one with bare eyes :).
For those of you wondeirng about the distinction between linear and circular: most essentially metering might get screwed up royally, and the auto focus might start hunting or take longer to lock on. For beginners to amateurs a circular version is thus highly recommended.
I did not have much time during the lunch break, the shot could have been aligned better, compare it to the picture above and you will see a big change in transparency with just a twist on the filter thread.