Circus Brat

She was born in the wagon of a traveling show

Her mama used to dance for the money they'd throw.
—Cher, "Gypsies, Tramps, and Thieves"

The Circus Brat is someone who grew up in a traveling circus. Usually part of a long legacy of performers, and occasionally gypsies and mystics. This is becoming less used as traditional circuses become less popular, but it is useful for establishing a bunch of things about the character. Often, polar opposites of the Military Brat:

Having an upbringing that was very relaxed.
Being very liberal and accepting of differences and others, what with hanging around with the bearded lady and conjoined twins year-round.
Frequent moves have left the character highly street-smart and savvy about traveling.
Character will have an excuse for knowing a variety of obscure but useful skills like juggling, sleight of hand, acrobatics, exotic animal care, performing and the like.
May be tired of being seen as a freak without solid roots and wish to be normal.
The circus brat sometimes has parents who work with the circus, but "running away and joining the circus" is also a trope, so there are also many runaways and orphans in the circus.

This is still a valid origin story in many fantasy settings pre-Industrial revolution, where television and video games haven't become wide spread.

This trope often applies to the children of carnies as well.

Examples of Circus Brat include:

Anime and Manga

Pictured above: Rita from Michiko to Hatchin.
Allen from D.Gray-man.
Claire in Baccano! grew up at a circus and worked as an acrobat, gaining a Charles Atlas Superpower in the process. He's also Ax Crazy, but that's not connected to his background.
Nadia from Nadia: The Secret of Blue Water.
Another Rita: Rita Rossi from Ashita no Nadja. Twice, actually: the circus owned by her parents got burned down, and since they died in that same fire she was taken in by other performers.
- Also Kennosuke and Nadja themselves. They weren't raised in the circus, but work there.
Goh from Yellow.
Marion Begnini from Kaleido Star, as well as Pamela's twin girls. Yuri and the Oswald siblings are more tragic examples: Yuri's dad died on-stage, and the Oswalds joined a circus after leaving their abusive step-parents.
Mai from Magical Star Magical Emi grew up in the Magic Carat Magic Show.
From Berserk Judeau spent his childhood with a traveling performance group and that may have been were his knife throwing skill was picked up. Puck also lived with the same group.
Sophia, a girl from an itinerant circus that a Magical Girl named Lunlun meets in her travels through Europe. In a subversion this does have repercusions in her emotional state, as she's stated to have few to no friends and refuses to work onstage as a clown, despite having inherited her Disappeared Dad's talent for acting and making people laugh.

Comic Books

Richard "Dick" Grayson, the original Robin from Batman. He still returns to the circus whenever they pass by Gotham and Bludhaven. He even ended up using his sizable trust fund to buy them out to save them from financial ruin.
- Originally Jason Todd, as Dick's Suspiciously Similar Replacement, was also this. He was given a completely different backstory after the Crisis reboot.
Nightcrawler / Kurt Wagner from X-Men.
Johnny Blaze, the original Ghost Rider. Stunt motorcyclist, later circus owner. Gives much plot in that the sideshow acts are often supernaturally real.
DC's first Trickster was a circus brat, which might explain his... eye-catching costume. Of course, this is DC...
Hawkeye and his brother Barney both grew up in the circus, and this is where Clint learned his sharpshooting skills to begin with.
The occult detective Hieronymus Bosch in the Danish comic with the same name was raised in a Russian circus by his acrobat mother and juggler father. He was trained in both conjuring and honest-to-karma real magic by the circus' illusionist, this being the original source of his occult knowledge.

Fan Works

Fear's back story as written in the Metal Gear Solid 3: Snake Eater fanfic The Joy of Battle was the son of two circus performers. It seems that he got his tongue from his mother and his ability to dislocate joints from his father. His story may or may not be based on Nightcrawler.

Film

The main character from Mirror Mask. She wants to run away from the circus and join real life though she seems to have come around by the end.
In Charlie's Angels: Full Throttle, the assassin known as the Thin Man is revealed (in a detailed flashback) to have been the child of Romanian circus performers who died in a fire.
On Ratatouille, Colette explains to Linguini the backstories of the other cooks. One was a circus acrobat who was fired for messing around with the ringmaster's daughter.

Literature

Kvothe from The Name of the Wind.
Kate from The Mysterious Benedict Society ran away to join the circus after her father left her as a baby.
The narrator and her siblings in the novel Geek Love. She's also a homegrown freak. Yeah.
The title character of The Phantom of the Opera grew up in a circus (as a freak) and learned a real skill with magic and choreography there. In the book, his first job after leaving the circus is as an entertainer/TortureTechnician for an Ottoman ruler.
In the James Bond novel The Man with the Golden Gun, Big Bad and Worthy Opponent / Shadow Archetype Francisco Scaramanga's parents were circus performers, and he worked both as a trick shot and an animal caretaker as a kid. His Start of Darkness happened when he shot a policeman for killing his favorite elephant when it went on a rampage.
Scharlotta Ivanovna, Anya's Cloudcuckoolander governess from Anton Chekhov's The Cherry Orchard. The second act of the play starts with her thinking out loud to herself about her circus childhood.

Scharlotta: (...) When I was a little girl my father and mother used to go round fairs and give very good performances and I used to do the salto mortale and various little things...

Parodied (with a partial reference to John Major's backstory, see below) in the Discworld novel Making Money. It turns out that Mr. Bent, the Obstructive Bureaucrat chief cashier was the illegitimate son of a particularly famous clown. Because of his natural talent for clowning, he was asked to perform after he reunited with his father; alas, he was traumatized because everybody was laughing at him, and they somehow neglected to warn him that it was supposed to happen. Bent ran away, and joined a group of Traveling Accountants, swearing off laughter, humor, and "silliness" for decades.
Eddie, the protagonist of The Five People You Meet In Heaven grew up (and spent the rest of his life) at a seaside amusement park. It was where he met his wife and eventually died; one of the eponymous people is the Blue Man from the freak show; a flashback shows Eddie using his ability to juggle to fight off his captors during the war in the Phillippines, etc.
The protagonist of Margaret Mahy's Maddigan's Fantasia, Garland, is the daughter of the titular circus' Ringmaster.
Bob Snarly from Anthony Horowitz' YA novel The Switch is close to a deconstruction of the trope. He's a brat raised by circus people alright, but he's far from open-minded, instead behaving like common trailer trash. An Aesop is learned.
Dorothy Shaw in Gentlemen Prefer Blondes.
Carlotta in Enid Blyton's St. Clare's series grew up in a circus. She keeps this a secret but is betrayed by the school sneak. Her friends, however, are thrilled by her exotic background.
One of the girls in a book called About Face grew up with a traveling circus when her dream is to stay in one town and own a house.

Video Games

Ellis from Battle Arena Toshinden. Thanks to horrific events in her past, her fa ther sent her to be raised anonymously as a dancer in a Turkish traveling circus in order to keep her safe from the mysterious organization hunting them. As result, she became an extremely skilled Dance Battler, arguably one of the fastest playable characters in the game and capable of jumps and acrobacies that actually makes the viewers think she can fly.
Razputin from Psychonauts. In an inversion, he ran away from the circus. He had a strict upbringing because his father was trying to prepare him for encounters with their family's many enemies, who were hinted at in a Sequel Hook that never took off, sadly.
Regina Berry in Phoenix Wright: Ace Attorney: Justice for All. She's very sheltered in many respects, such as having no concept of death and finding nothing strange about a marriage proposal from a ventriloquist's dummy. Not the performer, his dummy.
Jetta Maxx from Eternal Champions.
In at least one strategy guide, Doctor Neo Cortex of Crash Bandicoot is said to have been raised in a family of circus performers, and was literally branded a nerd due to his preference to science over the performing arts (hence the "N" on his forehead).
Sumire Nozaki in Tokimeki Memorial 2. A Secret Character in this game, she gets more spotlight in the Concept Art Gallery spin-off game Tokimeki Memorial 2 Music Video Clips : Circus de Aimashou.

Western Animation

School's Out: The Musical, a movie spawned from The Fairly Oddparents. Flappy Bob's childhood life as a clown and his secret love for it, despite his boring Pixie-life, is a vital part of the plot.
Princess Tenko of Tenko and the Guardians of the Magic grew up in a magic show.
Ty Lee of Avatar: The Last Airbender fame is this, by way of the 'ran away to join the circus' variant.
- It's implied she did this to stand out from her nearly-identical sisters-though it would be understandable if she did it to escape Azula.
  - This leads to her having traits of both I Just Want to Be Normal and I Just Want to Be Special.
Ernie Devlin in Devlin, as well as his siblings Sandy and Todd. Overlaps with Promotion to Parent as he had to raise them too.

Real Life

Sir John Major, Prime Minister of the United Kingdom from 1990-1997, was the son of a retired circus performer. This gave rise to the joke that he ran away from the circus to become an accountant.
Lots of early actors grew up in vaudeville and so forth. Buster Keaton started his career as a little boy being hurled around the stage by his father, learning how to fall so as not to break any bones and develop the Frozen Face that became his trademark.
The Byzantine Empress Theodora was the daughter of a bear trainer and had an early career as an actress (which in that time and place was a profession at least bordering on prostitution).
Renaissance Faire performers are a good modern expy. Some performers work within a local circuit, so not so much the traveling aspect, but they often come in families with the kids starting to perform as early as they can handle staying in a character. Other performers, especially established acts, travel 9–10 months out of the year to events all across the country.