Password/Funny

The Password is "funny". (ding)

Password CBS (1961-67)

May 29, 1962 (nighttime): Jack Benny gives the first clue for the word "Miser" — "Me!" The contestant's guess: "Ham."
March 10, 1963 (nighttime): During the intro, Bill Cullen introduces himself and says that "we're all here to pass Playword". Announcer Jack Clark laughs at Bill's gaffe, then introduces the show as Playword himself.
November 1966: During one episode, Frank Gorshin (who played the Riddler in Batman) got "Bat" as his first word in the Lightning Round. "Curses!"

Password ABC (1971-75)

December 1, 1972: The Odd Couple episode where Felix and Oscar play Password.

Password Plus (1979-82)

Just after winning $5,000 in Alphabetics, one champion tripped in the "hole" in the middle of the set (a small pit behind Allen's podium to make him not appear as tall) as she was walking to her seat. Allen even points out the purpose of said hole when she recovers.
Offering her guess to a Password Puzzle, a contestant asked "What are gymnastics?", causing Allen to quip "This is not Jeopardy!" He then turned to the board and asked, "Is it Jeopardy!?... oh, no, is it 'gymnastics?'"
December 23, 1980: In one round, Tom Kennedy couldn't stop laughing after Dick Martin's reaction to giving "French" as a clue for "France". It took nearly five minutes for everyone to get back on track. Betty White even got in on the humor by quipping that Allen Ludden (her then-husband, who was ill at the time) should trust that his show was in good hands.

Super Password (1984-89)

January 1985: Elaine Joyce and Tom Poston make a grand entrance through a stuck door.
Week of September 9–13, 1985: In an episode where Pat Sajak was a celebrity guest, they played the Wheel of Fortune puzzle reveal cue when the first password was shown. Cue Pat staring for a few seconds and then quipping that something sounded familiar.
August 25, 1986: Bert accidentally destroys the Magic Toaster. This was also an early example of the Running Gag of throwing a roll of tape at Bert if someone feared that he was about to blurt out the puzzle.
In general, almost any time Bert accidentally gave away the puzzle answer. This incident (week of March 9–13, 1987), where Bert accidentally gave the answer when suggesting a clue for the word "Flush", is perhaps one of his best:

Bert: But "royal flush" is a perfect clue for that word! That should not be the answer to the puzzle! I protest!
(audience applauds)
Bert: What did you want them to do? Go for "Toilet" for "Flush"? I mean, come on! You couldn't give a classy clue.
Gene Wood: You just gave away the second puzzle!

January 21, 1988: On an episode with Rip Taylor and Patty Duke, the password was "Testimony", to which Taylor gave the rather unhelpful clue "Episcopalian". After his partner failed to guess what the password was, Bert nearly gave it away himself but was stopped at the last second by one of the production team. Then, to cap things off, Patty blurted out "Testimony" to her partner when taking her turn, which caused Taylor to hit the Berserk Button, remove his toupee, and thrust it on the desk. Bert seized it and put it on his chest.

Bert: I've always wanted hair on my chest!

March 24, 1989: The Super finale featured Betty White playing what would end up being the last Cashword. Upon failing to get the word ("Shrewd"), Betty tore up the check slotted inside and threw the Magic Toaster II out onto the floor, nearly hitting a camera. Bert, apparently sensing that the show wouldn't have time to play the game again, handed the (mostly undamaged) Toaster back to her — and she proceeded to throw it again to the floor, breaking it into several pieces, to the applause of the audience (and the Mother Mackenzie machine).

Million-Dollar Password (2008-09)

(Nothing as of yet, but here just in case.)