Object Mode and Edit Mode
The 3D cursor is the most intuitive of the pivot points. With the 3D cursor selected as the active pivot point (from either the Editor's Header or via Period), simply position the 3D cursor and then do the required transformation. All rotation and scaling transformations will now be done relative to the location of the 3D cursor.
The image below shows the difference when rotating an object around the median point (right) and around the 3D cursor (left).