Its the copper contacts inside the solenoid that wear. The starter motor does have brushes, but they last a very long time and the sypmtom of worn brushes is a slow-cranking starter (gets sloer and slower over time).

Worn contacts are very common, the click-and-no-crank is the common symptom, what you are hearing is the solenoid plunger pulling in, but since the contact is worn out, the electrical contact is not made and thus the starter motor gets no current. The "click" is always there, but since the starter motor is normally cranking over the engine, you just don't hear it. However, without the noise of the cranking starter, you now hear the loud click of the solenoid.

Best bet is to do the troubleshooting steps listed on my page, or at least pull the starter out and open the up the solenoid and see if the contacts are gone. That way you'll know that:
#1 they are the cause of the problem (they may not be)
#2 whether one or both are worn
#3 which type you need, 4 basic shapes: