Another important point to note regarding origin is its use when using the mirror modifier, since the mirror is opposite the object origin on any axis.

For example, in Object mode if you create a brand new cube that is placed at the default center origin on the grid.. and then you try to use the mirror modifier.. nothing will appear to happen even if you have all three of the axis selected. This is because the origin of the cube defaults to the center of the geometry and therefore the mirrored cube is directly on top of itself, regardless of its actual location. Now move that cube to the left or right a bit... center the 3d cursor (if it has moved... with "Shift+C") and then press "CTRL+ALT+SHIT+C" and select "Origin to 3D Cursor." By moving the origin of the cube, you have just informed Blender from where to mirror from.

If you are ever having an issue with the mirror modifier, it is important to keep this in mind.