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John Wilkes Booth justifies his murder by calling Lincoln a tyrant, butcher, war-mongerer, and so forth. His high-minded rhetoric is undercut when he calls Lincoln a nigger-lover.
Sam Byck drops one at the beginning of "Another National Anthem":
"Where's my prize? ... I want my prize ... Don't I get a prize? ... I deserve a fucking prize!"
In H.M.S. Pinafore, Captain Corcoran, who "hardly ever says a big, big, D," is responsible for the one and only instance of swearing in the Gilbert and Sullivan canon: "Why damme, it's too bad!" It's still enough to shock the rest of the cast.
Though it's not in the text of The Pirates of Penzance, many productions have the exasperated Major-General shouting, "But damme, you don't go!" near the end of the ensemble "When the foeman bares his steel."
Also, in Utopia Ltd., King Paramount says "da-" twice, but is cut off before he can finish.
Any time Eddie swears in Blood Brothers. It's not like the other characters don't mouth off from time to time, but somehow it's far more shocking (and funny) to hear the middle-class, BBC-English-speaking Edward Lyons shouting "WELL SHAG THE VICAR!" at the top of his voice.
Frank-N-Furter: It's something you'll get used to! A mental mind fuck can be nice!
In the "The Gin Game" a man and a woman in a nursing home are playing gin against each other. He constantly uses the F word on her because she keeps winning. At one point he is so nasty to her she says, but unable to find a strong enough word to adequately describe him, "You are a horrible person, you... you... You FUCK!" She then is shocked, admitting it's the only time she ever used the word.
One of the most audience-startling moments in George Bernard Shaw's Pygmalion when it was first produced was when Liza, conversing with Freddy and his mother in a scrupulously refined accent, suddenly dropped the word "bloody".
Somewhat surprisingly, Jerry Springer: The Opera. The show is famously rich in profanity which should dilute its impact, but the song "I just wanna dance" manages to pull off a Precision F Strike with full emotional effect.
Shawntel:I wanna do some living, 'cause I've done enough dying. I just wanna dance. I just wanna fucking dance.
In Spamalot, King Arthur has a solo number bemoaning how alone he is... right in front of his horse/servant/squire, who gets increasingly frustrated by this as the song goes on.
Arthur: I'm all alone...
Patsy: Oh no you're not!
Arthur: So all alone...
Patsy: I'm HERE, you twat!
Sadly bowdlerized in West Side Story: Stephen Sondheim originally wrote the last like of "Gee, Officer Krupke" as "Gee, Office Krupke, FUCK YOU!" but was forced to change it to the very silly "Krup you!", much to his chagrin at the time.
He later admitted it was actually quite clever, he just really wanted to be the first in musical theatre to have a character say "fuck" on Broadway.
At the end of the play Oleanna by David Mamet, you can hear what is quite possibly the best line uttered by any character anywhere. The teacher, John, holds a chair above his head, aiming it at his former student Carol and utters the line, "I wouldn't touch you with a ten foot pole, you little cunt!".
Vanities: "Big fucking deal!"(Joanne in Scene 2) "Whoa, oh shit!"(Joanne again, near the end of "The Same Old Music") "What shit will you say next?"(Mary in "The Argument") "Trying to figure out what the fuck to do."(Joanne again, in the final scene/epilogue)
In Working, the truckers use the f-word freely, but we expect that kind of language from a truck driver. When the schoolteacher says "damn", however, it's shocking because we aren't expecting it from her.
The last act of Nixon In China has perhaps the first such example in the history of opera: "We'll teach these motherfuckers howitzer to dance!" The fact that said line is sung by a coloratura soprano makes it all the better.
Cathy uses this at least twice during The Last Five Years, specifically in the songs "See I'm Smiling" and "Climbing Uphill":
"You could stay with your wife on her fucking birthday, and you could, God-forbid, even see my show!"
"Don't look at my resume, I made up half my resume! Stop looking at that, look at me! No, not at my shoes, I hate these fucking shoes!"
The cast of I Love You Because manages to keep a show revolving around sex pretty clean for the first act, but soon into the second, as Austin is beginning to discover his feelings for Marcy:
Jeff: Can't you just FUCK SOMEBODY?
In Athol Fugard's My Children! My Africa, the white South African heroine begins the play apologizing for her language when she uses the word "hell." By the end, when she finally understands how devastating apartheid has been for South Africa, she storms out with a furious "This fucking country!" The line would be effective on its own, but it's especially powerful contrasted with her earlier apologies.
The current canon of Chess (established in the 2008 Royal Albert Hall concert) has this moment:
Anatoly: What about Florence's father? My wife and my children?
Freddie: Oh fuck you. You let them all down already. Win or betray yourself too.
The 1988 Broadway production had an entirely different one (though Freddie again, of course) in the scene before 'No Contest':
Freddie: …tell the Secretary of State that I am very busy, and that he can FUCK HIMSELF.
Walter: Okay, I’ll do that. Maybe not in those exact words.
In Les Misérables, Mme. Thénardier has this in Master of the House. "Master of the house, isn't worth me spit. Comforter, philosopher and lifelong SHIT!"
In RENT, Maureen shouts "That FUCK!" when the crew finds out that Benny locked the apartment.
In Roger Waters' The Wall Live tour, the lyric "Mother, should I trust the government?" is accompanied by the phrase "NO FUCKING WAY" appearing in bright red graffiti on the eponymous Wall.
In The Fix, Cal accidentally says "fuck" in front of the press while on the city council. However, he manages to turn it into a show-stopping number about how he's a straight-shooting, plain-spoken guy. It works.