Polarizing Filter. One of the most popular filters, a polarizing filter works like a pair of sunglasses for your lens. It adds saturation to your colors, especially blues, and cuts through reflections from water and bright white objects. Look for a circular polarizing filter that screws right onto the front element of your lens, the filter has an outer ring that turns, giving you different results depending on how it is lined up with the sun. A mark on the outside of the filter helps you to line it up with the sun giving you the most benefits. You can always saturate your colors in your images in post processing but being able to cut through a reflection from a body of water and see what is under the water, can not be replicated with software. Cutting the bright glare from white objects is also an advantage you get from a polarizing filter that is hard to duplicate with software.
Neutral Density and Graduated Neutral Density** filters are basic filters used by landscape photographers. A neutral density filter is grey and comes in different strengths allowing you to make images during the day with longer exposures so you can capture things like a flowing waterfall in bright daylight. You can stack different densities of neutral density filters to get different effects. A variation on the neutral density filter is the graduated neutral density filter. As its name suggests the graduated neutral density filter gradually goes from dark to clear.