I understood quite readily how having and empty in the shape of a single arrow or naked axes can help simplifying the 3D display but I shamefully fail to see the point of having empties that look like circles, spheres, cubes, cones… custom I can figure out.
Could you lit up my lantern?
Thanks for your time.
Jean
If I recall correctly, those shapes can be useful for animators. It is possible to use them to replace bone shapes in a rig.
This is a nice feature, already present in version 2.45 (Editing context > Armature Bones panel > the OB: field where one enters the name of a mesh to take the place of a bone in ObjectMode and PoseMode.
But I am referring to Editing context (F9) > Links and Materials panel, with an empty as the active selection. The choices in 2.45 are Arrows/Single Arrow/Plain Axes. To those of Circle/Sphere/Cube/Cone have been added. I think that you had the right intuition by thinking that the purpose is animation relates as Josuah took immediately interest in it as the animation system refactor that he is. I just can’t pinpoint their purpose myself.
Jean
Say you have a scene with a billion objects everywhere. An object can be made out of hundreds of parts. So what do you do to make your scene easier to work with? I would parent every little part of those objects to an empty. But if the scene contains 100 empties it’s hard to tell what objects is parented to it.
So if you can give the empties a shape that better match what it’s controlling, you get less guessing work.
For example - a tower gets a cone shaped empty, while a pool filled with balls have a sphere shaped empty.
And you maybe don’t want or have time to make custom shapes for every empty.
I hope your not fumble in the dark anymore 
No I ain’t anymo’ sir!
This lantern may just come in quite handily sometimes… especially if I can use a custom shape.
Thanks quite considerably.
Now I have to pull my car out of the last 30cm+ storm, second of the year, to go to my workplace.
I wish you a better wintertime than this. 
Jean