The Alice Network: Every character (not including background characters) has a tragic past and psychological issues, including Finn, a Shell-Shocked Veteran and ex-convict with anger issues; Charlie, a grieving pregnant teen; Eve, an ex-spy who's been through torture and has had more or less every friend she's made leave her; Cameron, another ex-convict with PTSD; and numerous others.
Pepys Road, the setting and focal point of John Lanchester's novel Capital, is a near-literal example.
Lampshaded in Peter Watts's Rifters Trilogy, particularely the first book, Starfish: several of the main characters got their jobs as "rifters" - deep-ocean explorers and colonists - by being too dysfunctional to fit in anywhere else; the theory is that those conditioned by their upbringing to accept undue stress as a normal living condition are actually more able to cope in extraordinary environments. This backfires more or less exactly the way you'd expect it to. Well, except that it's a Peter Watts book, so it backfires more or less exactly the way you'd expect it to except more so.
Ironically, the protagonist turns out to be so messed up not so much because her father abused her as because her employers surgically tampered with her brain to make her think her father abused her before sending her down there. Her parents turn out to have been fine and upstanding people. Which, in a Peter Watts book, makes them unique.
Those characters who are perfectly fine in House of Leaves are those who haven't encountered, spent time in, or explored the titular house, or, by proxy, read Zampanò's manuscript about the film about the house.
A Song of Ice and Fire is interesting in that half the cast are in the process of gaining their horrifically tragic backstories to become properly accredited as mentally scarred. The other half already has their trauma all sorted, and is busy topping up on additional horror to keep their various issues up-to-code and up-to-date. Westeros is, in short, not a happy, calm place to be. If the outside world doesn't find ways to mess with your psychological make-up (and, it has many, many ways to do that, given the wars, the openly biased (and generally disorganised and dehumanising) social and cultural institutions, the extremely casual violence, the lack of anything remotely like impartial justice, the rise of the dangerously supernatural, etc, etc, etc), your family can generally fill any possible gaps in your screwed-upness education by itself. The Lannisters, Baratheons, Greyjoys, Boltons, Targaryens, Freys and Craster's little incestuously cultish trainwreck are particularly good at giving each other reasons. But, the Cleganes, arguably, take the cake by actively, and intensively, training each other to become psychological wrecks of The Brute variety.
Justified in The War Against the Chtorr. 60% of the world population has died in a series of plagues, so all the survivors are walking wounded. This materialises in everything from sexual obsessives to zombie-like herds of people; and suicide is the leading cause of death even in the middle of the war. It's even suggested these psychological conditions are another type of plague created by the alien invaders.
There are a lot of messed up or incredibly depressed characters in Warrior Cats, but mostly in the third series. Examples:
Mostly caused by the fact that the author does not like happy endings. Quoting one of the other authors:
Cherith Baldry: I've heard it said that if you met your characters in real life they would attack you for treating them so badly!
Most of the villains in the series: Brokenstar was raised by an unloving mother, Tigerstar's father abandonned him to live with Twolegs, possibly causing his irrational hatred for kittypets, Scourge was abused by his brother and sister and ran away from home as a kit, Hawkfrost is mostly open for interpretation, but his relationship with his father is anything but healthy, and he seems to have quite the superiority complex.
Sunrise managed to mess up the lives of every main character from the second series.
Instead of just killing off main characters' love interests like she used to, the author has decided to create circumstances where they simply cannot be together, or their relationship gets killed, and they all end up with some kind of problem. This has happened, to some extent, to every major pairing from the second series onward (one of the most extreme cases being Lionblaze and Heathertail, who want to kill each other now).
Leafpool has been hit by Deus Angst Machinatwice all because of a single decision she made a long time ago. In Sunrise it was practically stated that she was suicidal.
Crowfeather, who has lost his two loves and now is paired with a cat who could be considered his friend at best, and is stuck with a bratty son who he neglects and abuses. He also refuses to acknowledge that he is still in love with Leafpool or that he has three other kits.
Breezepelt also has some issues because of Crowfeather's abuse. It seems that he has finally snapped under the weight of being unloved, and seems to have sworn revenge against everyone that he believes denied him the right to a happy life.
Cinderpelt's leg was run over by a car when she was an apprentice, crippling her for life and destroying her dreams of being a warrior. Then, when she dies, she is reincarnated as her neice, who then breaks the exact same leg and is almost subjected to the same fate as Cinderpelt.
Stormfur has been an outsider all his life. His mother died giving birth to him, and his father abandonned him when he was an apprentice, leaving him and his sister as outcasts in RiverClan. Then later on, his sister, who he was much closer to than anyone else, dies, he falls in love with Brook and leaves the Clans to join the Tribe of Rushing Water, which he is soon exiled from. He eventually goes back to live with the Tribe, but the last few chapters of Outcast makes it seem like the Tribe isn't going to be able to survive much longer.
Jayfeather and his various attitude problems originating from his dislike of being blind. As a little kitten, he actually says "I wish I had never been born!"
Sorreltail comes from one of the biggest families in the series, and now only has two blood relatives left. Within her lifetime six of her close relatives have died, and they are normally killed of within months of each other. One of her brothers' deaths could even be considered Death by Irony.
Well, not even bothering to use the Word of God relations, she still has: Cinderheart, Poppyfrost, Cherrykit, Molekit, Brambleclaw, Tawnypelt, Tigerheart, Dawnpelt, Flametail (not anymore), Mothwing, Mistystar, and Reedwhisker. Only five of them are in her Clan, but still, it's not that bad.
Dysfunction is the rule rather than the exception in Harry Potter. It's most noticeable with the Blacks, the Gaunts, and the Dumbledores, but every significant character has some family trauma in their backstory — and if they don't have it by the beginning of Book Seven, they sure will by the end of it.
Even the characters with normal families where no one dies will have trauma. For example, if she did it without their consent, what is Hermione going to tell her folks when she restores their memories?
In the X-Wing Series, the Wraiths are an X-Wing squadron composed initially of nothing but the Commander, his old wingmate, and people on their Last-Second Chance, in the belief that they will work hard to prove their worth. The author, Aaron Allston, is a big believer in using a Cast of Snowflakes. Everyone has something wrong with them. Otherwise they wouldn't be a Wraith. The commander does notice that they're actually good for each other, able to help one another get past their pasts and presents rather than making things worse. Still, the reputation sticks. When a new pilot is transferred in who was assigned because of their track record and not because of big screwups, a pilot jokingly says that he's too normal for the Wraiths. The new pilot then proves to be a Large Ham.
"Excuse me! Elassar Targon, MASTER OF THE UNIVERSE, reporting for duty!"
In the Witcher saga the group that helps Geralt in his quest to rescue Ciri has some of it. They're pretty concious about it.
Done very well in Doctrine of Labyrinths series by Sarah Monette. The main characters are especially dysfunctional; going into detail on how monumentally screwed-up Felix and Mildmay are would take a very, very long time.
If a character in A Series of Unfortunate Events doesn't have a Dark and Troubled Past, chances are they'll have something traumatic happen to them in the main story, with Count Olaf being the cause of most of it. Most of the adults have a Dark and Troubled Past due to their involvement from an early age with V.F.D. And the main characters lose their parents in the first book in a fire that burned down their house, spend almost every book being pursued by Count Olaf, a greedy psychopath who is after their fortune, lose countless guardians and friends thanks to Olaf's interventions, face kidnapping, one is almost decapitated by her sibling and if not for her quick thinking is almost made to marry above greedy psychopath (who blackmails her with the life of her sister), they are unjustly accused of murder and forced to commit arson to maintain a disguise, get thrown down an elevator shaft by their "guardian", are forced to do chores for a town that's acting as their guardians, thrown into prison, and are nearly killed by said town by being burned at the stake, accidentally kill a man, nearly die in the last book from being infected with the spores of poisonous mushrooms while stranded on an island... One almost wishes they died in the fire with their parents so they wouldn't be put through all this... because life sucks in their world.
The Glass Menagerie: There are really only four characters in the play but three of them, namely Amanda Wingfield and her two children Tom and Laura all have significant problems which seemed to be set into motion ever since the father left and their relationship with each other became strained.
The Doctor Who Expanded UniverseEighth Doctor Adventures were generally like this. The Doctor was constantly The Woobie, with enough issues to be his own personal walking Dysfunction Junction by the end of the series. He lost a wife and daughter in two entirely separate incidents, not to mention his memory and oneof hishearts. Fitz, one of his companions, seemed at times to be competing with him to be the most woobie. He grew up half-German during World War II and subsequently in foster homes, because his dad was dead and his mum was crazy. Then he met the Doctor, who killed his mum (and before that, he'd seemed to be a rather endearing and justified-by-her-neediness variant on the Momma's Boy). Cloning Blues and Cartwright Curse ensued. This overload of issues may explain why he never got a chance to worry much about his crush on the Doctor. After the seemingly wholesome and cheerful Soapbox Sadie discovered she had issues too and left, they were joined by a copy of a copy of a copy etc. of a Deadpan Snarker, who started out a Broken Bird and just got worse, really, no thanks to the Doctor. And then there was Anji, who seemed just peachy until her boyfriend of four years died. And then there was the fact that her whole childhood, the other kids picked on her for being Indian. Oddly, Fitz and Anji never seemed to commiserate about that similarity. And Trix pulled a bit of a Multiple-Choice Past and was never quite clear about it, and Anji suspected that her Broken Bird act was just a trick to get Fitz to like her, but she also had Sticky Fingers, and it was implied she'd been a sex worker at some point...
Their predecessors, the Doctor Who New Adventures, weren't much better. Over the course of the books, Seventh did quite a few morally questionable things, which would leave him wondering just how close he was to going over to The Dark Side. While he wasn't quite the woobie Eighth was, thanks to aforementioned morally dubious schemes, he got put through the proverbial grinder quite a few times in the course of events. Ace's parental issues had been established in the TV series, but in the books, the Doctor arranged the death of her current boyfriend, causing her to leave the TARDIS for several books and come back a hardbitten mercenary who took a long time to reconcile with the Doctor. Bernice could probably rival Fitz in terms of just how many issues she had, mainly relating to her childhood involving an interstellar war, a dead mother and a Disappeared Dad. Roz was seriously unlucky in love; she killed her first partner - a man she loved deeply - when she found out he was corrupt, then got it wiped from her memory by the Big Bad. Another of her love interests turned out to be a murderer; Roz being a by-the-book cop, this did not sit well with her. About the only one who was left untouched was Chris... up until Roz died, anyway.
Hoo boy, Ironman. (no, not that one.) The main character is an antisocial sports nut who suffers an inferiority complex due to his father's borderline draconian discipline policies. And his anger management group? One's a nihilistic Jerkass, one's a confrontational punk with a Hair-Trigger Temper, and the last one is a Cloudcuckoolander who is completely incapable of rational thought and can only spout inane gibberish due to having suffered years of horrific torture from his psychopathic father.
Wicked Lovely. Let's list how: Aislinn has a dead mother and Disappeared Dad. Keenan has a dead dad, and an abusive mom. Seth has serious Parental Abandonment issues. We don't know much about Donia's past, but the curse that put her in constant pain for nearly a century is hardly productive to a happy life. Leslie has a Missing Mom, neglectful alcoholic father, abusive druggie older brother, and was raped before the start of book two. Niall also has Rape as Backstory, as well as being in love with the one who let it happen, a major Guilt Complex, and Reluctant Monster syndrome. I could go on.
Animorphs. We have a leader who struggles with his own decisions and has an older brother as the enemy, a Machiavellian-esque Sad Clown who's willing to kill his own alien-possesed mother, a Blood Knight who's worried about losing control, an emotional wreck who's stuck in hawk form and is happy that way, an animal rights girl who can play you like a piano and an Amusing Alien who lives in the shadow of his deceased brother. And they're supposed to protect us. Our world is in good hands.
The Dresden Files. The hero is orphaned, abused, betrayed by his father figure and girlfriend, and nearly executed - all by the time he's sixteen. And let's not even go into what happens to him after the books start.
Leaving that aside, there's also the amount of screwed up families: the Raiths (daughters raped once they hit puberty, sons killed off) and the McCoys (Gramps is the White Council's assassin, Mom hung out with an evil crowd and got herself killed, sons have parental issues, crappy luck and crappier love lives, and granddaughter was kidnapped by vampires for use in profane ritual) to name two. The Carpenters are surprisingly well-adjusted considering Dad is always off battling the forces of evil, but even they've got some major dysfunction in the form of Charity and Molly. Charity still has issues stemming from a near-brush with Black Magic as a teenager, and Molly's teenage rebellion leaves her teetering on the edge of The Dark Side even before Harry's death in Changes turns her into a full-on Broken Bird.
The Book of Joe has a cast full of characters struggling with their issues, with Joe still coming to terms with his past, Wayne living with AIDS, Brad's marital problems, Carly disastrous former marriage and so forth.
The Fire-Us Trilogy is set in a Teenage Wasteland where 90% of the characters would be institutionalized if institutions still existed. Among the main cast we have Teacher (The Insomniac of the obsessive variety who spends all her time writing in their Great Big Book of Everything and then forgetting what she wrote, "discovering" it, and interpreting it as prophecy), Mommy (an Hikikomori with a "screaming spirit" that sometimes overwhelms her, leading her to attack and threaten to kill others), Angerman (a schizophrenic who is convinced his mannequin caused the deadly virus and is now out to kill all of them if they aren't careful), Cory (an ex-cultist), Baby and Doll (two girls who are emotionally and mentally stunted, maybe due to being raised by the older kids), Action Figure (a young boy who's essentially gone feral), Teddy Bear (who's scared of almost everything and in particular of alligators), and Puppy and Kitty (two children who really were feral and speak only in barks and meows. Then you meet the Keepers of the Flame.
In C. S. Lewis's The Four Loves, he observes that nothing is more natural for a child to feel no love for a parent who isn't loveable.
Seth, Regine and Tomasz of More Than This all died as children, so it's not so surprising that they had tough lives. As Tomasz comments: "Are we not some funny kind of group? Child abuse, murder and suicide."
Almost all the Greasers in The Outsiders fit this. Ponyboy, Sodapop and Darry lost their parents in a car accident. Steve has an abusive father. Johnny's parents abuse him and constantly neglect him. Dally has a growing criminal record since he was ten and used to run with gangs in New York. Only Two-Bit seems to have a mostly happy childhood.
The Swedish police as portrayed in the Backstrom novels is full of barely functioning coppers who all have their own preoccupations and limitations — the appalling Ewart Bäckström is merely the most obvious one.