I don't want the bone to change the direction it's pointing. In other words, I want it to be able to rotate, not translate.

Use the constraint "roll like" to whatever bone (target bone) you want it to "roll like". Do not use "orient like".

The bone that you have constrained to roll like the target bone will not translate if you translate the target bone. If you also use the constraint "Translate to" the target bone, then the bone will also translate.

I may be misunderstanding you but I don't want the bone to roll like another bone. I only want it to roll. Like, for example, a wheel on a car. But this is actually part of a joint on a robot's arm. It should only be able to rotate in one axis, whilst (I think I'm using that word correctly ) another part of the shoulder joint rotates along another axis.

If you only want a bone to rotate on 1 axis when animating - then you can change the manipulator options. See the screen capture, where I've restrained a bone to rotate only on the z axis

However if you are rigging something, and have a hierarachy of bones, I suspect you will have to use constraints, depending on your rig.

You would have to post what your model, rig looks like and what you are currently doing.

An Euler limit (constraint) will do the job.

Can yo show us what you are trying to do?

I'm sorry if my description of what I wanted wasn't clear. I found it though. I was looking for a spherical limit where the min and max longitude and latitude are 0 but the min and max rolls are -180 and 180 respectively.

The only think I wanted that bone to be able to do was roll, nothing else.