In digital photography these kinds of filters are generally useful in landscape, travel and architectural photos:
- Polarizing filters to darken the sky and reduce reflections off water, glass and other shiny objects.
- Neutral density filters to reduce the amount of light going through the lens, so you can maintain wide aperture and slow shutter speed in bright light
- Gradient neutral density filters to darken one part (e.g., bright sky) of scene while leaving the other part unaffected
- Gradient color filters (primarily blue, red, orange, pink) to selectively change part of an image (such as enhancing the color of sky or sunset).
Also, many people use a clear filter (e.g., UV filter) for lens protection, but many others don't believe in them because of the potential to degrade image quality.
When photographing people it is better to capture the best original quality you can and then make any adjustments in post processing.