A quick run down of the basic filters:
UV Filters were used on film to reduce haze, but don't on digital because the sensor has a UV filter anyway. Some still use them for protection but that's a can of worms you don't want to open
Circular polarisers can cut down reflections or amplify them in ways software can't replicate, and enhance colours. These are often used for landscapes (particularly shots with water)
ND (neutral density) filters are uniform filters that simply cut down the amount of light reaching the sensor so you can take longer exposures (good for making creamy smooth water surfaces)
ND grad filters have a gradient, so cut out light reaching the top parts of the image so you can expose for the sky at the same time as the ground (but if they are not used well the effect can be far too obvious).
There are also colour filters that are use for B&W photography to alter the luminance balance of the colours (for example a red filter would make blues darker and reds lighter), but these were mostly only used on film.
A lot of the effect of filters can be replicated (though not quite as well) in software.
Unless you have a specific requirement, you don't need a filter.
Joe
cheers