While many filter-like effects can be simulated with photo-editing software, there are three on-camera filters that might interest you: Neutral Colour, Neutral Density and polarizing. Neutral Colour (NC) filters are simply there to protect your lens.
In the film world, ‘Skylight’ or ‘UV’ filters are often used for this purpose but, since digital cameras have an internal UV filter in front of their sensor, the use of external UV filters is not recommended as it may cause colour problems. Neutral Density (ND) filters appear grey and are used to reduce the amount of light entering the lens. This can allow you to use a slower shutter speed for certain effects (see Photographing Water, below). Polarizing filters are often used to cut reflections from non-metallic objects, including water, and to increase the contrast between a blue sky and clouds. For auto-focus cameras, I recommend a ‘circular polarizing filter’. (A linear polarizing filter may, in some orientations, interfere with the autofocus mechanism).