The Pirates of Penzance, or: The Slave of Duty is a famous and much-parodied (and itself redolent with parodies and lampshade-hanging) operetta by Gilbert and Sullivan, and one of the most famous works of 19th century English drama. The eponymous slave to duty is Frederic, who was accidentally apprenticed to a pirate ship when he was a boy, and felt honour-bound to be the best pirate he could be — but now he has come of age, and his period of apprenticeship is over, he feels honour-bound to round up a posse and wipe the pirates from the face of the earth. Hilarity Ensues.One of the most widely-recognised bits of the operetta is the Patter Song "I am the very model of a modern major general", sung by the father of the obligatory love interest.
All There in the Script: The Pirate King and the Sergeant of Police have their names listed in the dramatis personae as Richard and Edward, respectively. This never comes up anywhere else.
Better yet, the Pirate King is regularly renamed Roderick because so many directors like to have Frederic, Ruth and the Pirate King perform some variation on "My Eyes Are Fully Opened" from Ruddigore.
Mabel: Oh, Frederic, cannot you, in the calm excellence of your wisdom, reconcile it with your conscience to say something that will relieve my father's sorrow?
A Running Gag throughout the play relies on the fact that in Victorian Received Pronunciation, the words "orphan" and "often" sounded the same. The jokes still kind of work, but it means stretching the sounds of the words to their limits.
Breaking the Fourth Wall: If it doesn't have it at some point, it's not true Pirates. Sorry. There is even a notable sword fight with the conductor. This has occurred in several versions—the movie even features it during the climax. It's also Older than They Think: it originated as a spur-of-the-moment outburst in the original production.
The 1994 Australian production (the one with Jon English and Toni Lamond) is filled to the brim with this, amongst Actor Allusions and Shout Outs aplenty. The revival production a decade later even referenced this — Jon English stops to make sure that a number of gags from the original aren't repeated, with the explanation "they've all seen the DVD anyway".
Calling Me a Logarithm: Depending on the production, this can be the pirates' reaction to Major-General Stanley asking "You're not thespians, are you?". The non-verbal reaction of Jon English, playing the Pirate King in Australian productions, is a comic masterpiece.
Deus ex Machina: The pirates finally surrender when asked to do so "in the name of the Queen". A deliberate parody of Victorianism.
General Stanley fails to notice the group of about two dozen pirates and policemen hiding (poorly) in his garden. On top of that, the pirates fail to notice the policemen. This despite all of them serving as chorus to General Stanley's song.
Flaw Exploitation: The Pirates themselves make a point of two things: 1. Never to attack a weaker party than themselves, and 2. Never to molest an orphan. Word gets around.
Also, it's common knowledge that every British person loves his queen.
Sung, of course, at the top of one's lungs. Often while performing a kick line.
"With cat-like tread, upon our prey we steal In silence dread, our cautious way we feel No sound at all, we never speak a word A fly's footfall would be distinctly heard!"
The Ingenue: Mabel: a young soprano winning the affection of the lead tenor, whose role calls for some terribly soprano-ey cadenza runs (which are hilarious).
Insane Troll Logic: Major-General Stanley claims the portraits in his house are of 'his ancestors', even though he bought the house and moved in recently and the portraits show ancestors of the family who previously lived there, because he bought the house, they're his portraits, so therefore they're his ancestors!
The 1994 Australian Production had the conductor force the pirates to perform four encores of With Catlike Tread.
Patter Song: The Major General's Song is a shining example of the craft.
Pair the Spares: General Stanley and Ruth are often paired off at the conclusion. (The policemen also end up gaining wives along with the pirates, depending on the male-to-female ratio of the cast.)
It can also depend on the director's sense of humor. One production had enough daughters for every pirate and every constable, but the Sergeant remained alone because the Pirate King grabbed two girls!
Pirate Girl: Although describing piratical maid-of-all-work Ruth as a 'girl' might be a bit of a stretch.
The Pirates Who Don't Do Anything: subverted, sort of- they attempt piratical activities, they're just useless at them, combining being very soft-hearted with being rather dim-witted.
Sergeant of Police: It is most distressing to us to be the agents whereby our erring fellow-creatures are deprived of that liberty which is so dear to us all— but we should have thought of that before we joined the force.
Skeleton Key: In the song, "With Cat-Like Tread", one of the pirates' tools mentioned is their "skeletonic keys."
Suddenly Suitable Suitor: In the final scene, Ruth reveals that all the pirates are "Noblemen who have gone wrong." The Major General is suddenly eager for the buccaneers to marry his daughters, as are the girls themselves. "With all our faults, we love our House Of Peers!" Gilbert and Sullivan used this trope regularly.
Swiper, No Swiping!: The pirates turn themselves in when requested to surrender in the name of Queen Victoria.
World of Ham: Oh yeah. Especially during the "With Catlike Tread" number.
This work is referenced in:
Kate and Leopold: Leopold gets the plot wrong. He describes the main character as the Pirate king who falls in love, and claims that the pirate king has never seen a woman. The character he was describing was actually Frederic, the apprentice pirate and main character. This is exceptionally funny, since Leopold is supposed to be very educated. The actor brother recognizes the plot as described, even though it's incorrect.
Doctor Who has a Sixth Doctor audio story called Doctor Who and the Pirates which turns into a piratical musical. In addition to using many tropes common to Musicals in general, including several lampshades about characters tendencies to break into song. The story even gives The Doctor the song, "I Am The Very Model of a Gallifreyan Buccaneer".
Runescape Has a song titled "The Pirates of Penance"
The West Wing episode "And It's Surely To Their Credit" has a Running Gag about the White House Counsel, Lionel Tribbey, mistakenly attributing "He Is An Englishman" to The Pirates of Penzance (it's actually from H.M.S. Pinafore). Nearly everyone in the cast points out his mistake and that all of Gilbert and Sullivan's work is about duty.
Frasier, niles and,...uh...Major Winchester are familiar with, among other Gilbert and Sullivan works, Pirates of Penzance. Martin—not so much.
Leland (singing):...With many cheerful facts about the square of the square of the hypotenuse!
Frasier, Niles, and Leland (harmonizing): With many cheerful facts about the square of the square of the hypotenuse, with many cheerful facts about the square of the square of the hypotenuse, with many cheerful facts about the square of the square of the hypotenuse!