I'd suggest a UV filter (or skylight filter as fotojack mentioned) to protect the lens, a circular polarizer for certain conditions outdoors, a neutral density filter so you can achieve slower shutter speeds (very helpful when the desired effect of waterfalls or other slow moving water images require a smoother, glassy appearance), and also a graduated neutral density filter for the times when the sky would normally come out overexposed (when it is too bright compared with the foreground).
The effects from a lot of other filters such as a warming filter, a tungsten filter, etc. can be achieved in post processing so not all filters are necessary.