Depends entirely upon conditions, but for "normal" situations - relatively dry, no snow or ice, no technical climbing, and a pack weight of less than twenty-five pounds or so, a good pair of running shoes does it for me. If the terrain is rocky and rough, I often go to a mid-weight, leather and fabric hiking boot boot. The most versatile is an approach shoe - for me they work for general hiking, bike riding (I still pedal in old style cage pedals) and lower grade rock climbing.

Stay away from high tops. They constrict your muscles and provide unnecessary weight. They are worthwhile in a work environment where you are swinging picks and shovels, etc.

The most important characteristic of any boot is fit. Your best bet is going to a good outdoor store and getting expert sizing there.