1965: Supposedly, the longest continual laughter in live TV goes to a Carson Tonight episode. His guest was actor/singer Ed Ames, who claimed that in the course of his work he had learned how to throw a tomahawk. Carson produced a human outline on a board, and Ames lobbed the tomahawk at it. It hit the board successfully, but slammed in right at the figure's crotch, starting the thunderous laughter. When the laughter started to die down, Carson quipped "I didn't even know you were Jewish!" starting it all up again. (Even funnier still was Carson's followup remark: "Welcome to Frontier Bris!")
1968: The Dragnetparody with Carson and Jack Webb. "Clean copper clappers."
1969: George Gobel's appearance, put in the impossible position of having to follow Bob Hope and Dean Martin. "Did you ever get the feeling that the world was a tuxedo and you were a pair of brown shoes?"
November 1979: Prior to Thanksgiving, Johnny talked with Doc Severinsen about their respective plans for the holiday. Before long the two of them had each other, and the audience, in stitches.
"Before Photoshop", but particularly when Conan showed a photo of Larry King at his desk, and the audience laughed. Conan found it amusing that they were laughing at an untouched photo and not the punchline.
Jimmy Fallon (2014-)
Jimmy's first night started with a bang. Besides him and Will Smith chronicling a history of hip-hop dances (ala Justin Timberlake and his and Jimmy's "History of Rap"), and U2 performing on the roof of 30 Rock, we have a moment where Jimmy mentions a "friend" who says he'd never host the Tonight Show, saying they owe him $100. Cue Robert De Niro, Tina Fey, Joe Namath, Rudy Giuliani, Mariah Carey, Tracy Morgan, Joan Rivers (in her 1st Tonight Show appearance, of any kind, since being banned from the show in 1986; the ban was kept by Leno out of respect to Johnny Carson), Kim Kardashian, Seth Rogen, Lindsay Lohan, Sarah Jessica Parker, Mike Tyson, and Lady Gaga all throwing crumpled C-Notes on the desk, culminating with Stephen Colbert pouring a bucket of 10,000 pennies on Jimmy's head, ending with "WELCOME TO 11:30, BITCH".