Henry's confrontation of the guy that groped Karen.
"I'm funny how?" - A scene that goes from Crowning Moment of Funny to deadly serious as Tommy, known for his anger issues, starts pressing Henry about a compliment seemingly gone wrong. After a minute of horrified silence, Henry figures out Tommy is only joking about being angry, and everyone starts laughing again... The most-remembered - and parodied - part of the entire movie.
Scorsese's level of Doing It for the Art, right down to actually playing Layla while shooting scenes for the montage so the music would perfectly match the shots in the exact manner he wanted.