Filters
One element which is often ignored when people learn about photography is filters; just as 75% of my large format images used view-camera movements, I would estimate that close to that many of my black and white images film used filters, as well as a fair number of my digital images (especially the water Nudes).
Current Filters
(Digital)
For my digital SLR cameras, I use two kinds of filters, neutral density and polarizer filters, both of which affect images in ways that post production cannot. Other traditional photo filters filters, used for changing image colour or contrast can be better done in post production, with digital images.
A neutral density filter is used to slow an exposure, permitting either a larger apertures for less shallower depth of field, or the use of longer shutter speeds, to emphasize motion. 
I carry 4x, 8x, 64x, and 1024x neutral density filters (which block 2, 3, 6 and 10 stops of light), which give me enough range of exposure modification for most situations.
A polarizer filter can be used to remove reflections from water or glass, and to saturate colours and the sky on sunny days (both effects that cannot be applied in post-processing of a digital image). While I carry three sized of polarizing filters, I seldom use them, preferring the natural rendition of tones to the altered perception of polarization (which is odd, given my love of working with infrared light.
I own complete sets of the above filters in three sizes, 58mm, 72mm and 77mm.
Film Photography
(1986-2005)
When I used film cameras, I worked with the following filters: Light Yellow, Yellow, Orange, Yellow-Green, 2x, 4x, 10x Neutral density, two ND graduated filters, two light-tobacco graduated filters, two yellow graduated filters, and a red graduated filter.
With colour film, filters are generally used to change the colour balance of an image - to compensate for the natural light (cooling morning or evening images, or warming mid-day images) or to over-emphasize the colour balance - creating a cold blue day, or a warm yellow sunset where none actually exists. 
In black and white, filters are used to change tonal relationships - a filter lightens its own colour, and darkens its opposites. Thus a yellow-green filter (one of my preferred filters) lightens green foliage, and darkens skies (blue is the opposite of yellow). The only drawback of using filters is that they reduce the amount of light falling on the film, from 1/2 a stop for a light-yellow filter, to three stops for a deep red filter.
For my 8"x10” view camera, I used two filters systems - a Cokin P series for my 300mm and 450mm large format lenses, and a Cokin X-Pro system for my 150mm view camera lens, because of the large (95mm) size of its front element. The X-Pro series covers lenses up to 122mm in diameter, and come in a wide variety of types.