These seem to be asked about quite often, so I decided some testing should be done to establish the facts about these items.
There are two types : linear and circular. Either type will work with a camcorder, but the circular type is recommended. This is because they usually work better with cameras that have auto-exposure and auto-focus. Several reputable sources have stated that a circular filter is the one to use with a camcorder. Additionally, linear filters only work with some cameras but circular filters work with all of them.
The difference between the two is something too lengthy to go into in full here, but if you would like to know please read this page : http://www.school.net.hk/photoweb/filters.htm .
Very basically, the filter only allows light through which is polarized in one direction. The linear filter passes it polarized while a circular filter uses a second layer to make the light no longer polarized once it enters the lens.
If you have a polarizing filter but are unsure which type it is, hold it up to your eye and look through it with that eye only at a mirror. A linear polarizer will look the same if you flip it over whereas a circular polarizer will look very much darker one way around than the other.
For the test, I used a Jessop JESCP37 37mm circular polarizer shown here:
The filter is a high quality piece with scratch resistant glass. The outer ring turns independently of the inner giving you the facility to change the direction of polarization once the filter is screwed on firmly.
I tested the filter outside with several different infrared filters and discovered that the filter slightly reduced the reflection and glare given by some types of material, particularly those with reasonably high percentage of polyester and similarly a fair amount of viscose in them. Overall, I have to say the results were somewhat disappointing.
The filter proved to be very effective at removing reflections from glass in windows and the surface of water. So much so that in some cases it is possible to see through a window when you could not before. However, this is already a well known use of a polarizer.
In conclusion I would say that the polarizer may increase your x-ray by a very small percentage on some garments which exhibit a shiny or glowing appearance. The filter itself is quite a cheap item and the first shop I went into had several in stock. If you don't mind a second filter showing on the front of your camera and you are likely to film around water or through glass then it might be worth it.
One last point worth noting is that the filter reduces the light level a little and may help users of semi-modified camcorders.