The first is the problem with the diaphram inside the ballcock (fillvalve). Often the diaphram drys out (looses its flexibility) from age. Once this happens, it cannot close properly, so it fluxuates as it tries to shut off. This sends a minute noise throughout the system, like the lips on a trumpet player vibrates. The sound amplifies through the pipes. Replaceing the ballcock solves the problem (an easy fix).
Another thing that can happen is debris broken loose from the water system (calcium and mineral deposits) can get inside the valve and begin to vibrate. The same effect happens as stated above. Removing the cap for the ballcock and flushing water through it often clears the problem.
Finally when you have a blocked vent or improper flow, the toilet can pop or make noise as it tries to flush.