Of all the filters available, a polarizing filter is the first one you should buy to improve your landscape photography.
So What Does It Do?
First of all it can darken blue skies turning them a deep, rich blue. Polarizing filters are also great for removing reflections in water. So if you're shooting a river scene and you want to see detail in the water or on the river bottom, a polarizer will reduce the reflections. They're also good with foliage, making leaves and such less shiny (again, cutting down on reflections). Color saturation is enhanced with almost any subject. No other filter can provide this.
The polarizing filter one thing and one thing well - it removes reflections from non-metallic surfaces:
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Skies
By eliminating the reflection of light on the tiny water droplets present in the atmosphere the polarizer brings more saturated and slighly darker skies.
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Water and reflective surfaces
By eliminating reflections, the polarizing filter will tend to make water and other reflective surfaces more transparent. The effect will also vary depending on the angle to the reflective surface. If you place your camera very low above a river, the effect will be very limited. If you shoot from a bridge above it, the water will look totally transparent.
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Color Enhancement
The polarizing filter also reduces reflection from other surfaces such as foliage and thus makes their colors look more intense. It also tends to make shadow areas darker.
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Light absorption
The main side-effect of the polarizing filter is that it absorbs 1.5 stop of light. So, if you shoot at 1/180th of a second and then add the filter, you will find yourself at 1/60th of a second. This happens whatever the orientation for a polarizer. In low light situations, some type of camera support, such as a tripod, will be needed.