This post is one of ten appearing in the series 10 Ways To Improve Your Landscape Photography. There is a misconception that you don't need filters in the digital age. An example would be that if you've got an overly bright sky you can just darken it in Photoshop when you get home rather than using a graduated filter. That may be true in some cases, but not all. Often the contrast range between the land and the sky is so great that your sky has either blown out (so no information to actually recover the sky in Photoshop) or the land is so dark as to be near black (and as a result very noisy when you later brighten it). Similarly the effects of full NDs and polarizers are difficult or impossible to replicate in post-processing.
The 3 most useful filters are described below.
Full ND (Neutral Density)
A full ND is a dark piece of glass or plastic the purpose of which is to reduce the amount of light entering the lens. It's basically a pair of sun glasses for your camera. The effect is to give you longer shutter speeds than would otherwise be possible. A classic example is when taking photographs of waterfalls where you use the ND filter to reduce the amount of light to get a shutter speed of 1sec or more to create the "silky water effect". I have a 3-stop ND in my kit
The grad is like the full ND except that it is clear at the bottom and dark at the top with a transition between the clear and dark in the middle of the filter.The main purpose of this is to make the bright sky darker to lower the contrast between the sky and the relatively darker land.
You can buy the filter in a variety of darknesses, normally 1-, 2- and 3-stop. You get a Hard grad which which has a very abrupt transition and Soft grad where the transition is more gradual. A Hard grad works better when you have a straight horizon where you can line up the transition line with the horizon. The Soft grad is more useful where you have objects (e.g. trees or mountains) that rise above the horizon line.
I have two Hard grads in my kit, a 2-stop and a 3-stop
Polarisers are like magic! There are a number of effects from using a polariser, the two key ones are increasing colour saturation and reducing or removing reflections in water.
I won't go into the science here but the way you use it is to rotate it to increase or decrease the effect. It is most effective at 90° to the sun. It can be a particularly useful tool for adding some punch when shooting during the day where it can give you more dramatic, deep blue skies.
Like tripods, filters slow you down. Unfortunately this can often be the "can't be bothered" type of slow down so it's important to know your system well. Since upgrading to the (unfortunately very expensive) Lee filter system I've found using filters much less of an annoyance.