The entire premise for many Dom Coms is that the lead characters are a family of maladjusted people who generally don't get along. Usually they consist of a Jaded Washout and/or Bumbling Dad father, a mother who is either a paragon of common sense and efficiency or a repulsive harridan (or both, a la Roseanne), and two-three kids who are unhappy, dislike each other, and resent at least one of their parents. Also, the father and his mother-in-law tend to hate each other. The family is generally fairly poor, although not always - Arrested Development is about a large, rich dysfunctional family.
Don't get them wrong, though; for all the family arguments, the typical dysfunctional family never engages in actual abusive behavior - any that did would immediately lose all audience sympathy. Furthermore, when the family is facing a major problem from outside, they will generally pull together to face it. Dysfunctional Families may not get along, but they rarely actually loathe each other, and often receive Aww, Look! They Really Do Love Each Other moments.
In American comedies this was originally a subversion of the Leave It To Beaver/The Brady Bunch almost-too-good-to-believe family, but eventually ballooned into a genre of its own. The Dysfunctional Family has been a British comedy staple since the 1950s.
Contrast with Quirky Household, where the people are merely weird, but generally happy — indeed, more happy than more conventional households.
See also Big Screwed-Up Family, who are more numerous, more dysfunctional, and not (usually) Played for Laughs.
Tsukihime reference: The Tohno Family who, due to their non-human ancestry, were a 'cursed' gene pool of insanity, various psychosis, and sanity-decaying superhuman abilities; their family tree was full of suicides, early deaths, disappearances, and the like. Needless to say, they didn't necessarily get along with each other, although they co-existed rather well.
The premise of The Daichis: Earth's Defense Family is one of these families being recruited as a pseudo-Super Sentai team just before the parents formally divorce each other - and the hilarity and angst that ensues.
Ranma ½ has two of these; the Tendos and the Saotomes.
The Tendos consist of: the over-emotional father, Soun Tendo, who bursts into a geyser of tears at little provocation. The eldest daughter, Kasumi Tendo, who is a Yamato Nadeshiko so sweet and nice she frankly comes off as deliberately oblivious at times. The middle daughter, Nabiki Tendo, a mercenary money-maker and teenage seductress who will happily sell skimpy photos of and paid dates with her little sister and her little sister's fiancÚ alike for extra pocket money. And the youngest daughter, Akane Tendo, an emotionally unstable and verytsunderetomboy martial artist.
And these two families are arranged to marry each other. Specifically, Akane Tendo is supposed to marry Ranma Saotome. If they can ever sort out the Love Dodecahedron in favor of that particular pairing.
In the Josei manga With The Light, (almost) each child or parent Sachiko encounters has a dysfunctional family. One chapter had the saddest way to start: a father is stinking drunk and the son tries to run away- only to see his mother escaping asap in a taxi- leaving him alone. Another child, Eri-chan, refused to tell a teacher about Hikaru, an autistic boy, getting seriously hurt in fear that her father would hit her "just like he hits mommy".
Oyasumi Punpun has a more serious version of this trope. Mom and Dad are divorced after an incident of domestic abuse, Uncle is a serial cheater, and poor Punpun is raped by his aunt. They do care about each other, but most of them have too many issues to express it in a healthy manner.
Well, it certainly helps explain some things about Harley Quinn. In Gotham City Sirens we learn that her father is a con-artist who abandoned his family to scheme older women out of their fortunes, her brother is a shiftless deadbeat with multiple kids from different mothers and no job, and her mother might be suffering from Manic/Depressive Bi-Polar disorder. One of the reasons Harleen Quinzel became a psychiatrist in the first place, which was the first step on her trip to becoming Harley Quinn, was to try and understand all the emotional trauma her family put themselves and each other through.
The Fantastic Four of Marvel Comics fame were designed to be a rather dysfunctional and constantly bickering, but ultimately tight-knit and loving family unit, which is part of what made the comic so popular and part of what put Marvel Comics on the map; the fact that each member has superpowers only adds to the tensions and clashes between them. Although only Susan and Johnny were initially directly related to each other (sister and brother), Susan and Reed later married and started their own family.
Reed and Ben are the type of best friends that are so close they each consider the other their brother, blood relations be damned, making the Four all in-laws. Which explains a lot about all their conflicts, actually...
A running joke about their dynamics is the fact that their teamwork is so phenomenal and their Power of Friendship so strong in the face of danger that it has become legendary, yet they can barely function without constantly screaming at each other or stewing in bottled fury over personal conflicts whenever things are quiet.
The Bat-family has become this in the last few years. There's a lot between just the men of the family. First you have Batman, an absentee father. His jerkass moments far outweigh his nice moments regarding his family, since he works alone. Needless to say, this messes up the family pretty badly. There's also Jason Todd, who holds a grudge against Bats for not avenging his death, and has a one-sided rivalry with Nightwing, akin to a little brother hating his Aloof Big Brother. Finally, there's Damian, who desperately seeks Bats' approval to the point where he assaulted his brothers. The only member of the family he gets along with other than Bats himself is Nightwing, who was his Parental Substitute for quite some time. Needless to say, it's quite amazing that Nightwing is so well adjusted, seeing the family he comes from.
The central branch of the Achike family from Purple Hibiscus. Father is a religious maniac, Mother is regularly beaten but too frightened of him to say anything but still considers herself lucky to be his wife, daughter is almost mute from terror and only the eldest son recognizes that something is really very wrong. Or so it is at the beginning of the novel, anyway.
Sherlock Holmes and Mycroft Holmes had a sibling rivalry which affected the entire family.
The Trethowans from Robert Barnard's mystery novel Death by Sheer Torture. The author bases them on the real-life family, the Mitfords.
In Michael Flynn's Up Jim River, Zorba explains Bridget's silence by this: the Hounds are like brothers and sisters, but there is a certain amount of sibling rivalry.
Reversed in The Addams Family and The Munsters, both families are wildly dysfunctional in the classical sense, but treat each other with respect and love. That it's expressed via poisoning, stabbing, and other grievous and macabre means is just funny.
In 3rd Rock from the Sun the aliens resemble this. In one episode, they use it as a cover for their odd behavior when they become the subject of a documentary on dysfunctional families.
Everybody Loves Raymond, although it focuses more on the adults than on the kids. Actually, if you think of Frank and Marie as the "parents" and their children and their girlfriends/wives as the "kids", you have two generations of this represented.
Not when you consider that Ray's kids are inexplicably normal; the fact that they're also inexplicably Aryan compared to their parents, may have something to do with why these apples fell so far from such a crooked tree.
The Monk family in the Crime Dramedy series Monk is heavily implied to be dysfunctional. The parents raised their kids, Adrian Monk and Ambrose Monk, in a very strict fashion, which evidentally contributed to their quirks (such as Adrian Monk's various phobias and Obsessive Compulsive Disorder, as well as Ambrose Monk's Agoraphobia), their father, Jack Monk, eventually and inexplicably left the family in 1972 while going to get Chinese Food, which also resulted in Ambrose and their mother becoming cataconic. Their Christmases were also heavily implied to be horrible experiences for Monk. Jack Monk's other family, Jack Jr. was also proven to be no different. Although Jack Monk mentioned that Jack Jr. was a heart surgeon in Baltimore, it was later revealed in the same episode that Jack Monk lied about that out of shame, and that Jack Jr. was actually a putz (actually, not even a putz, but a person who dreams of one day becoming a putz), who lives in his basement, smokes Marijuana, and steals from Jack's wallet, and also had a criminal record of selling stolen cars and intends to move to Paraguay.
On the kids' sci-fi show Halfway Across The Galaxy And Turn Left the main family consists of a gambling-addicted father, a scatterbrained mother, a dreamy Cloud Cuckoolander older sister, and a child genius younger brother. The family relies on its middle child, ten-year-old X, to run their daily lives whilst adapting to Earth culture and keeping them safe from the wrath of the Zyrgonian Government. The strain of running her family actually makes X physically ill.
The Crane family from Frasier is a mild version (seeing as they are as close-knit as they are combative), with the "children" starting as adults in their late 30s. Their dysfunction is exacerbated at the beginning by the fact that the family's late matriarch Hester Crane was the lynchpin that held her sons and her husband together, and Frasier and Niles' Sibling Team dynamic had been put on hold during Frasier's decade-long absence. One of the show's underlying story arcs, especially in the first couple of seasons, involves Frasier and Niles rebuilding a close relationship with their father in the absence of their mother to facilitate things.
Game Of Thrones. Every family, but particularly the Lannisters, the Targaryens, and the Freys. In fact, the Starks are the more close to a happy family in the story, at least at first.
The Paolo Family, from The Amazing Race Family Edition, spent their time on the race bickering and yelling.
Next To Normal: "So my son's a little shit, my husband's boring, and my daughter, though a genius, is a freak."
That's only the first song. Later songs reveal that the daughter is nearly cracking under overwhelming perfectionism, the husband is expertly codependent, and the mother has been suffering hallucinations for sixteen years — because the son is dead.
Apparently, King Boo is the father of Mr. Doom's Boo. Pink Boo is either his girlfriend, wife or ex-wife, and all the little mini-Boos are their kids. This doesn't stop them from giving him crap; instead, they're constantly after him to pay child support instead of spending all his coins to support his Star habit.
The Simpsons: The obvious exemplar, we could be here all day with examples to back up their inclusion. However, even if the President wished Americans could be "more like The Waltons and less like The Simpsons," they stay together, go to church together and eat dinner together every night, and they're ultimately closely-knit.
Daria. Here, the central character's family, the Morgendorffers, are seemingly screwed up; but the family of Daria's best friend - the Lanes - is far worse, to the point that they're the former Trope Namers for Hands Off Parenting.
South Park: All the families in South Park, Colorado.
Moral Orel lives and breathes this trope, though it's more the "Idyllic outside, dysfunctional inside" version.
The Petes on Goof Troop consist of a father who abuses one child while spoiling the other when he's not neglecting both of them (Pete), a mother who is usually yelling at her husband and daughter (Peg), a son who is emotionally damaged, disillusioned with his father, and impatient to leave home (PJ), and a Bratty Half-Pint daughter who gets on everyone's nerves (Pistol). They are the foil family for the main Quirky Household from whom the show takes its name, and when PJ is in focus (and occasionally when he's not) it's portrayed more as a Big Screwed-Up Family.