At the near-conclusion of the episode where Sheriff Kirk is Drunk with Power, trying run the Fonz out of town and bullying everyone else, and EVERYONE is dressed in leather jackets to stop the overbearing officer.
The dance contest episode is about to end with everyone content, and the contest not mattering. However, Fonzie has been roped into being Marion's dance partner, and is none too happy with the idea, that after all the grief in the episode, his efforts are just going to waste.
Another dancing moment occurs in "They Shoot Fonzies, Don't They?", during a dance marathon at Arnold's. Fonzie, having already gone through hell and back just to get to Arnold's, is wiped out by the time he and another couple (consisting of the Alpha Bitch of Joanie's school and her dumb boyfriend) are the only ones left on the floor. He's about to be carried off in the customary stretcher when said Alpha Bitch makes reference to a prior bet the two couples had made, where if Fonzie and Joanie lose, Fonzie gets a crew cut. Cue Fonzie hollering "CREW CUT?!", forcing himself off the stretcher, challenging the other couple to a special "challenge dance", and wiping the floor with them.
Fonzie saving Joanie from being raped. He did nothing but kick the door down walk between her and her would be rapist and stare him down. That sick freak was so scared, he jumped out a window.
Any moment with Fonzie coming to the rescue qualifies.
Special mention must go to Richie, Potsie, and Ralph for taking on a gang alone in "Joanie's Weird Boyfriend."