Color film or digital - (as you identified) circular polarizers and neutral density (full and graduated):
Polarizers: Use circular polarizers. The effect is slightly less than linear polarizers, but the AF and exposure of modern cameras (which use partially reflective mirrors) do not work well with the linear variety. They block indirect reflections when used with natural light. Polarizers also reduce the brightness of the sky. This effect is best at 90 degrees from the sun, and diminishes at angles other than that. Normal and telephoto lenses do not show enough of the sky to notice any weirdness, just a darker sky, so these work well with these lenses and polarizer filters outdoors. Wide angle lenses will show an unevenly lit sky, which may add drama to the shot, or it may look cheesy. You decide.
Indoors, polarizers reduce indirect reflections, such as on metallic or plastic surfaces. When polaroid sheets are placed over the light sources at 90 degrees to the lens filter (known as cross polarization), specular reflections of the light source can be eliminated from shiny surfaces. This is especially useful with glass items.
Neutral density filters: These reduce the light over the entire spectral range consistently. Beware of filters which have a color cast, but with digital, you should be able to correct this by setting a white balance reference through the filter. Use a ND filter to get a longer shutter speed with a larger aperture, especially useful when shooting with flash on a camera which has a long sync speed.
Graduated Neutral Density Filters: Used to lighten a portion of the scene with respect to another area of the scene. For example a ND grad can be positioned over the sky portion of a landscape to give more exposure to the ground part. This will prevent the ground from being lost in the shadows, and the sky from being blown out white. The best ND Grads (as they are known) are rectangular filters which can be positioned at any angle and height on the lens with either a special holder, or by hand. This will allow the photographer to use them with subjects which are not split right down the center. ND grads come in several strengths, designated by the stops of difference between the halves of the filter. I'd suggest at least a 3 stop difference to get the best effect.
Other filters: Color filters will add a color cast, half magnifying filters will allow half of the scene to be a close-up with the rest to be distant, star and halo effect filters add spectral and multiple image effects, and cylindrical lens filters will "drag" a portion of the subject to simulate movement. Some of these effects can be simulated with software, but sometimes it's so much simpler to get it right in the camera!