What a polarizer does is eliminate light reflected from the surface of objects at a certain angle. It works very well on the sky too. So if you are indoors and you adjust the polarizing angle you can cancel out the reflected light of a window or table or whatever at the cost of a light loss. When you filter out the reflected light colors tend to saturate. Be aware it doesn't eliminate specular reflections.

I often use a polarizer indoors if I am using studio lights to match indoor light intensity to that of the outdoors- specifically when views through a window are important to an indoor setting.  In most cases the affect of the polarizer on the outdoors, as seen through the window, adds measurably to the results.

Hank

definitley better than the hammer approach.

I shot some frames at a cabaret show with my G2 and inadvertently left the circular polarizer in place.

I seem to have lost about a stop but otherwise it was hard to see any difference after downloading.

Has anyone ever done this on purpose?

The worst thing a polarizer can do to you is act like a 1 stop neutral density filter, unless you are trying to photograph reflections. I have a polarizer stuck on my 35-350mm f3.5-5.6L (it's a long, sad story, please don't ask) and the only time it bothers me is when working in low light and I would like the extra stop of speed.

Jonathan, I don't know the actual problem you have with your stuck filter, but when I get a filter stuck I use two rubber bands.  Put one band on the lens and one on the non-rotating portion of your filter, and then try to unscrew the filter.  The extra grip provided by the rubber bands has always worked for me.