Hari:*laughs* I had a great childhood. Where do you think I learned how to fight? By the time I was eight, I knew: Every fight is a fight to the death.
Is happy and even proud of their Dark and Troubled Past, believing that their trial by fire makes them superior. This may make them cocky, but they usually have the savvy and muscle to back up their arrogance.
Frequently Antiheroes. The degree to which the character is well-adjusted versus is harboring a lot of pain inside depends on the writer. See also Wrong Side of the Tracks, Neighbourhood Friendly Gangsters. As children they are more likely to have been The Artful Dodger rather than the Street Urchin, but the Dodger is more of a trickster where the Street Rat is more of a cutthroat. May have been raised by The Fagin. Those who knew the Street Rat as a more vulnerable child may see them as a case of From Nobody to Nightmare in adulthood.
Fabiola is a subversion. Fabiola grew up under similar circumstances to Revy but still clings to *some* degree of morality. Granted in Black Lagoon, that's not saying much...
Puli, the nine-year-old leprous gang leader in the book Nectar In A Sieve, is deeply cynical and deeply proud of how hardened he's become. (He winds up saving the heroine with his skills, although he doesn't do anything for free.)
Briar Moss of the Circle of Magic starts out like this, and opens up as time goes on. He stays tough as nails, however.
Both Bean and his arch-enemy, Achilles, show elements of this, having spent their early years fighting to survive on the streets. Bean is more well-adjusted and doesn't seem to dwell on it much. Achilles turned out to be a complete sociopath who just CAN'T let anyone who has ever seen him in a position of weakness live very long.
Part of his obsession with Bean seems to stem from just how frequently Bean has PUT HIM in positions of weakness.
Ferro Maljinn of The First Law. Her background went from war slave to harem mistress to murderous desert fugitive with a vendetta, but the core personality fits this trope spot on.
Hissune from Lord Valentines Castle is this, played straight in the novel itself, while in the sequel it's subverted as all hell, when Lord Valentine makes him a nobleman and eventually Valentine's successor as king of Majipoor.
Demetrios Makropolous in "A Coffin for Demetrios" (filmed as "The Mask of Demetrios" with Peter Lorre, Sidney Greenstreet and Zachary Scott). Demetrios goes from poor fig packer to murderer, smuggler, assassin and spy.
Tabletop Games
Iconic character Dai Blackthorn from GURPS is based on this archetype.
A very common PC background, especially for characters with stealth or other 'thief' abilities. Because living family is basically bait for a GM to kidnap them and force you to rescue them, but angst annoys the other players, an orphan or abandoned child that's not particularly broken up about it is a good way to avoid your character's backstory interfering with the campaign.
The "Earthborn" origin for Shepard implies Shepard used to fit this archetype(or still does, if you play an unapologetic renegade path). In the first game, Shepard can even run into a friend from his old gang.
Web Comics
Quain'tana of Drowtales grew up on the streets with no apparent parents and eventually rose to be one of the greatest war leaders in the worldsetting. Her first "pack" was composed of other street rats that eventually grew into a mercenary empire, but unlike other examples her lack of parental figures really takes its toll on her children.
Doc Worth from Hanna Is Not a Boy's Name partly fits: he has the less-than-legal job and is proud of it and his dingy place. It is unknown what his chidhood or relationship with his family were like, but they were well-off enough to pay off hi med school expenses.
Web Original
Mimeo of the Whateley Universe. His childhood consisted of being a numbers runner on the streets of New York City, right up until he was told to kill some people or be killed. He gained superpowers and managed to avoid the problem, by putting his father and two assassins in the hospital. He's a super villain who will do pretty much anything except kill people, and he has selfish reasons for holding back on that account.
Western Animation
Megatron of Transformers Prime wears his life as "a gladiator from the pits of Kaon" as a badge of pride despite the fact that he was a slave because of it.
In Avatar The Last Airbender, Zuko (before his "World of Cardboard" Speech) believes that his psychotic father somehow made him stronger, despite the fact that said father burned Zuko's face and banished him for speaking out of turn. Zuko says this in the first season: "I don't want luck, I don't need it. I've always had to fight and struggle. It's made me strong, it's made me who I am." It's made clear, though, that a lot of his pride at his past is him lying to himself, as he doesn't want to acknowledge that Ozai is evil.
Real Life
Truth in Television - People born and raised in the Mexico City barrio of Tepito are characteristically proud of their lifestyle.
This applies to many sorts of 'rough neighborhoods,' really, such as Bed-Stuy, Chicago, Detroit, or South Central. It doesn't always have to be violent, however. One can find many examples among workaholics who credit their work ethic to being from Appalachia or Mississippi.
Similar to the above example with Megatron, many gladiators came to embrace the lifestyle and adoration of the crowd. If such a thing existed today, (or if they allowed such to compete in the NFL) it would be similar to a prison football team wanting life in prison because of all the fans they get by actually being the prison's football team.