This happens in Turn-A Gundam when the queen of the Moonrace decides to switch places with a lookalike on a whim. This has severe repercussions on both characters and on the war between the Moonrace and Earthrace, ultimately culminating in the lookalike going to be Queen of the Moonrace in the actual queen's place
The Pokémon episode "Dawn of a Royal Day!" (pictured above) had Dawn trade places with Princess Salvia - who wanted to participate in a Pokémon contest - who then gave her Togekiss to Dawn to gain experience as she traveled.
This trope deconstructed is the premise of Barrage: Prince Barrage finds Astro, a boy from the slums who looks and sounds exactly like him, and forces Astro to take his place as prince while Barrage runs off intending to lead a life of hedonism—but Barrage gets assassinated by a sniper as he's leaving and disappears off the rooftops they're on. This effectively forces Astro to impersonate Barrage to keep the kingdom's political enemies at bay. Those closest to Prince Barrage knew immediately that Astro was an impostor but have agreed to keep the façade as well for the same reasons. Then it's subverted: Astro is the true Prince. His Parental Substitute and mentor kidnapped him from the palace and replaced him with a doppelganger made of dark power and raised Astro in the slums to spare him the court's manipulations.
In one Archie comic, Lil Archie agrees to take the place of a weary prince who is identical to him. Lil Archie then successfully puts down an uprising, while the Prince is off enjoying his freedom.
Bunty, a British comic for girls, used this plot a few times. One recurring strip involved a wealthy Victorian heiress switching places with her maid for a day, but then the maid steals a valuable heirloom belonging to the heiress and claims to be her. The real heiress is forced to remain as a servant until she can find a way to prove her identity.
The old UK Anthology ComicNipper (1987) had a strip called "Will & Bill", in which a working class kid who looked identical to the then-five-year-old Prince William would exchange places with him.
Trading Places plays with this; the people aren't physically identical. Instead, two really rich old guys are pulling the strings.
The various versions of The Parent Trap, including a movie starring the Olsen Twins circa age 11, use a variant on this plot in which each of the swapped characters is both "prince" and "pauper" at the same time.
And, in all versions except the Olsen Twin one (which was titled It Takes Two), the protagonists were related. Incidentally, the only film versions to actually have twins playing twins were the original Das doppelte Lottchen, and the 1953 UK version Twice Upon A Time.
And there's also the original bookDas doppelte Lottchen, published in English as Lottie and Lisa.
The Lizzie McGuire Movie had Lizzie impersonate an Italian pop singer, because another idol wanted to ruin the real ones career when he in fact lip syncs.
The Little Rascals short "Alfalfa's Double" has a rich kid named Cornelius from another neighborhood who looks just like Alfalfa. When he bumps into Alfalfa they decide to swap roles. Hilarity Ensues.
The Great Dictator, where Charlie Chaplin plays both a Hitler-esque dictator and a Jewish barber, naturally ends up like this.
Class Act has a juvenile delinquent and a genius high school student end up swapping roles when their pictures are swopped on their school records.
''Dave is a 1993 film about Dave Kovic (Kevin Kline), who is hired for a night to replace President Bill Mitchell (also Kline) to cover up an affair. After the president unexpectedly suffers a stroke during sex with his mistress, Kovic becomes the "real" president and gets to work.
Summertime Switch is another non-identical version of the plot: an orphaned delinquent and a spoiled rich kid are being sent to a juvenile detention center and a luxury summer camp respectively for the summer. However, since they both have the same name (Fred Egan), there is a mix up at the bus terminal and they end up switching places.
Clambake, in which Elvis, heir to an oil fortune, switches places with Will Hutchins, water ski instructor, in order to prove he can win the girl and win the race without Daddy's money.
The trope is named for a Mark Twain novel in which Street Urchin Tom Canty gets mixed up with Prince Edward VI of England.
An element that rarely get used in other works is that both try to come clean and get it reversed. Of course, even at the crowning ceremony no-one takes the pretender seriously that he isn't really the prince until the real one shows up.
Quoted, played straight, subverted, lampshaded, deconstructed, and reconstructed in Billy and Howard. Repeatedly.
This is the main plot element of Anthony Hope's 1894 novel "The Prisoner of Zenda" (and the subsequent film)
A similar plot is used by Robert A. Heinlein in Double Star (although, to be fair, in this novel the duplicate is an actor, who uses his own skill at acting rather than merely accidentally being a body double)
Happens in the Narnia book The Horse and His Boy, with Shasta and Corin. It turns out, though, that the "pauper" is actually the rightful prince, and the "prince" is just his few-minutes-younger identical twin. Said twin is happy to find this out because it means he doesn't have to bother with the responsibility of being king.
Happens in the Myth Adventures novel Hit or Myth, where King Roderick convinces protagonist Skeeve, the court magician, to temporarily take his place using illusion magic. Of course, Skeeve finds out a little too late that the King did it because he was due to be married to the queen of a neighboring kingdom who's rumored to be insanely greedy and bloodthirsty. It turns out that the Queen IS ambitious and clever, but not evil, and catches on to the switch instantly...but when she shows more interest in marrying Skeeve than the King, the conflict becomes finding the King and getting him back to the wedding without the Queen finding out and killing him.
Buffy the Vampire Slayer: As part of a plan to masquerade as her twin, Vampire Willow, Willow is obliged to swap her fuzzy sweater for leather bondage attire.
Willow: I guess vampires really don't have to breathe." [glances down] "Gosh, look at those."
The trope is taken to a new level in "Warrior... Princess... Tramp..." and in yet another new in "Warrior... Priestess... Tramp..."
In the third season The Man from U.N.C.L.E. episode "The Galatea Affair", U.N.C.L.E. agent Mark Slate is tasked with teaching working-class Bronx bar performer Rosie Shlagenheimer to act like THRUSH minion Baroness Bibi De Chasseur (both roles played by Joan Collins).
This concept is used in a Wishbone episode where he is telling the story.
The Monkees episode "The Prince and the Paupers", where Davy impersonates a prince to help him get married.
in the 1896 John Philip Sousa opera "El Capitain," Don Enrico Medgua, the Viceroy of Peru, doubles for "El Capitain," the leader of the rebellion against the Spanish rule in Peru.
The Moxy Früvous song "King of Spain" is all about this:
"Prince and pauper Junior and Whopper World made up of Silver and copper Under my own volition I took a change of position!"
Used in The Story of Evil whenRillianne, who was a terrible ruler switches places with her servant and twin brother, Allen. A bit unusual in that this is not the beginning of the plot, but rather the dramatic climax of it and that Allen himself organizes the whole thing to save her from an uprizing. Under the Princess' guise he gets captured and promptly decapitated while the Princess successfully escapes. In a later song Rillianne is shown being burdened with regrets over his death, though, and in the finale she becomes a lowly nun in a monastery.
The Zany Scheme subplot of The Taming of the Shrew, wherein Lucentio (son of a wealthy merchant from Pisa) and Tranio (his servant) switch clothes upon arriving in Padua. Tranio takes on Lucentio's identity while Lucentio pretends to be a tutor. (Whether the two actually resemble each other depends on your interpretation of the line "We have not yet been seen in any house/Nor can we be distinguished by our faces/For man or master". Regardless, it's clear that they get away with the switch because no one in Padua knows them, and in performance they generally look nothing alike.)
Played with The Royal Trap - from the beginning, there are rumors that Princess Cassidy is an impostor, and there just happens to be a similarly-pink-haired commoner girl in the cast being treated unusually well by the King and Queen. The whole story is... complicated.
Johnny: Wanna experience life as a commoner, I know.
Prince: Am I really that transparent?
Johnny: Naw, I just seen a lot of TV.
In the Teenage Mutant Ninja Turtles episode "April's Fool", Shredder kidnaps April confusing her for a princess, in order to get a jewel as ransom. It's played with in this case; April shows up for a party in a pretty dress, and because it's fancy dress, she's the only person there dressed like royalty. Meanwhile, the princess gets pissed off with all the parties, and sneaks out dressed as an ordinary person. The two don't actually see each other until near the end, and April never expresses a desire to be a princess.
Done in The Simpsons, with Bart swapping places with a rich kid... whose siblings are trying to kill him.
The VeggieTales video "Princess and the Popstar - A Story of Trading Places."
In an episode of The Hub's Pound Puppies, team member Squirt and high society pooch Mr. Cuddlesworth switch places after meeting at the shelter when the latter chihuahua runs away from his home.
Open Season 3, where Boog the bear is accidentally mistaken for a Russian circus bear who looked exactly like him, while the real Russian bear simultaneously traded places with him so that he can live in the wild.
The Pink Panther and Sons episode "Millionaire Murfel" had Murfel trading places with a millionaire.
A Jem episode featured a Princess who looked like Kimber.
The Proud Family: Mariah Carey's pet monkey and Oscar's Mr. Chips had this forced onto each other when Oscar, while distracted by Carey's presence at the vet's office, threw an injured Mr. Chips into a sick room that was already occupied by Carey's monkey (who was sick due to eating Proud Snacks). Things go uphill for Mr. Chips (who is mistaken by Carey for her pet), and downhill for her pet, with the latter experiencing something close to slave labor regarding meals, and later having its piano playing skills exploited for cash. Things end up back to normal after the pet finds Mr. Chips and takes back his identity forcefully and returns to his rightful owner, and Chips to his.
Done in an episode of Popeye & Son with Junior and a prince.
In Johnny Test episode Princess Johnny, Johnny is asked by Men in Black and White to impersonate a missing princess to avert a war. The princess (Who looks like Johnny with lipstick) is found in an arcade; She ran off to 'be a normal kid'.