My only 'must have' filter is a circular polarizer...which is especially good for outdoor shots like landscapes.
If you want to take some long exposure shots (of running water / water falls) then you might also consider a ND (neutral density) filter as well.
Split or Grad filters can also be good for landscape type shots...but I tend not to use them because I usually don't shoot landscapes that have flat horizons.
If you are planning to shoot in rough situations, you might want to consider a UV filter, just to protect the front of the lens.