Updated: Oct 15, 2019
Another advantage of a DSLR is the number and variety of filters available. These are relatively inexpensive but provide much more variation to your picture. In fact, if you want to take landscape shots, filters are VERY important as they can make or break some of your shots. A landscape photographer without a full filter kit is a landscape photographer without a hand!
The broad categories of filters are:
Graduated Filters -- allow you to "hold back light" on parts of your image. Useful for high conrast lighting control
Neutral Density Filters -- use these to get that silky effect on water because you can increase exposure time
Polarizer Filters -- gives the sky a saturated blue look, reduces glare and reflections, and saturates your image
Color Filters -- can warm or cool an image
UV Filters -- stops UV from entering the picture. Most photographers use these to protect the camera lens, however
As a landscape photographer, your bread and butter filters will be Graduated Filters, Polarizer Filters, UV Filters, and to some extend, UV Filters. Depending on what you want to do, you may find a lot of use for some of the specialty filters too.
If you've ever wondered WHY you can't seem to get a balanced landscape picture with a baby blue sky and well exposed foreground or that perfect sunset where the sky is vivid and colorful AND the foreground is not too dark? The secret is to use a GRAD Filter (Graduated Filter). These filters help you "hold back" the light in key areas of a photo. This lets you take a more balanced image, even when there is high contrasting light, such as during sunsets.
A polarizing filter is also another very useful filter. It will for example make blue skies much richer and will balance color compositions. Even with an inexpensive 18-55 mm lens that comes as part of the default camera kit lenses when you buy a starter Nikon or Canon DSLR package, it's always a good idea to use a UV filter to protect the lens and CCD from sunlight damage. This is particularly relevant for landscapes where long exposure times may be required.