I like to simplify my shooting and since I switched over to digital, I no longer need to carry a load of filters. When shooting film, I used a plethora of filters because to loosely paraphrase a computer term "What you shot was what you got!"
I believe that a digital photographer can get away with only two or three filters (not counting a protection filter which you may or may not desire to use).
The three filters which are useful:
1. Circular polarizer (CPL) - this filter can provide effects which CANNOT be duplicated in photoshop such as reducing/removing reflections in windows or the surface of the water so that you can see what is behind the windows or under the water. The CPL will also remove/reduce reflections from foliage (especially wet foliage) and intensify the color. It will darken the skies and reduce or prevent burn sky burn out. IF YOU HAVE ONLY ONE FILTER - THIS IS THE ONE TO HAVE. Buy the very best you can afford since cheaper GND filters will degrade the imagery - sometimes with terrible effects.. It is often less expensive to purchase the CPL online than in your local store.
2. Neutral density filter (ND) - this filter will reduce the light levels without modifying the color. I use it most often to allow me to slow the shutter speed enough to blur running water and waterfalls. I wish that the "Canon Gods" would allow an ISO 25 capability with their 1.6x cameras. Then I could normally dispense with the ND filter. It is actually possible to combine two polarizing filters (one must be a circular polarizer and the other a linear polarizer) to achieve a variable neutral density filter. Linear polarizers cannot normally be used with auto focus or auto-exposure cameras so used ones are available dirt cheap.
Create Your Own Variable Neutral Density Filter
3. Graduated Neutral Density FILTER (GND) - the purpose of this filter is to reduce the exposure of the sky while leaving the foreground normal. It is most often used for landscapes and comes in a hard cut-off (which is good for seascapes because the horizon is strictly delineated) and a soft cut-off (which is better for landscapes). I blow hot and cold on using GND filters. The round GND filters are a PITA because the line of demarcation is directly through the middle of the filter. This means that you have to compose your image with the horizon centered or do some heavy cropping. Square GND filters either need a special adapter or you need to hand hold the filter in front of the lens. This causes problems with using a lenshood. You can achieve a lot of the effect of a GND filter through photoshopping. I don't carry a GND unless I am specifically shooting landscapes.
Since I have a lot of filters left from my film days, there are two general types which are fun to shoot with:
Star Filter: This filter causes the four, six or eight pointed stars (depending on the filter used) around lights. It can be absolutely great on images with a single or only a few light sources. It can be overwhelming when used on an image with a plethora of lights - such as a city scape. I would not necessarily buy a filter of this type but, it can be fun to use.
Diffusion filter and or fog filter: there are several types of filters of this type which give a bluring effect to the image. They are nice for portraits and give a dreamy effect to landscapes. Again, I would not necessarily purchase one of these but, I have a couple and they are fun to experiment with. One warning: "What you shoot is what you got!" You cannot sharpen an image that has been creatively blurred with one of these filters. You can often find a used one at a fairly low price. Since the object of this filter is to give a blurring effect, IMO, you don't need the best quality filter available.
Ladies Hose: if you stretch a piece of ladies stocking material over the front of your lens, it will give a softening effect and occasionally a star-like effect. It can also warm your image or give a ND-type effect; depending on the color of the recycled hosiery material. This is an old-time method.
You can achieve the above using Photoshop but, it is a lot easier and aften more fun to play with a filter of some type.