Despite his clear misery over his baldness, Homer has never bothered with wearing a toupee. This is parodied in one episode where Mr Burns and the Rich Texan are engaging in a scavenger hunt, one of the items being "Homer Hairs". After both of them pluck off Homer's remaining hairs, Homer runs into a nearby hair salon and buys a wig that looks exactly like his own bald scalp, complete with the now missing hairs.
During a science fair, Nelson has a "wig detector" that's just a bunch of stuff taped together and Nelson himself makes beeping sounds while pointing the "detector" at whatever he believes to be a wig. When Superintendent Chalmers shows up wearing a wig that doesn't match his receding hairline, Nelson makes beeping noises at it until Chalmers removes the wig. Nelson then makes beeping noises at the receding hairline until Chalmers removes it as well.