As you know, I am not a fan of leaving UV filters on your camera all the time – they can increase flare.
And a polarizing filter (a dar-looking filter that can turn) should definitely not be left on, because it eats several stops of light. But it does have its uses. Main among these: make a blue sky more saturated blue.
Like this “blaah” sky of last May (oh how I wish it was May again):
Put on a polarizer (“c-pol”); turn it just right; and voila:
Note that this works best at angles perpendicular to the sun. If the sun is right in front of you, or right behind you, the polarizer will not do much. This also means that very wide lenses will give you an uneven sky.
But yes, carry a polarizer for your lenses (other than the widest, perhaps). For this and other uses, too, like removing reflections off non-metallic surfaces.