"Johnny Angel" is a hereditary superhero, with three generations of Belluci men playing him, only one of whom has a power and is not a Badass Normal. The lone female, Bella, is not a superhero but has a superpower (luck/electricity).
The Quicke/Dash/Caleb family. All but one member of the family (and with regards to her, who knows?) is a superhero.
In Touch, we have the Toranagas, a family of the strongest mages in the eastern United States, including Peter, a doting father who also happens to work as a director for The Men in Black, Hideyoshi and Tsuru, a pair of immortal, monster hunting grandparents, and James, a twelve year old boy with levitation and mass-scale aerokinesis. His younger sister, Bex, is implied to be just as powerful.
The only exception to the badassery is the mom, Sarah, who, while she might not be a powerful mage, still manages to pull off some moments of awesomeness herself.
The Potters themselves don't do too badly either. James and Lily are a Battle Couple who also thrice defied Voldemort and (although unbeknownst to them) were the parents of the one who eventually killed him. Then, Harry marries into the Weasley family...
The Carpenters. Dad's the Fist of God, Mom's his sparring partner, blacksmith, and an incredible Mama Bear who assaulted the castle of the Winter Queen, and the oldest kid has a natural talent for magic, and is now Lady Winter.. Also, they've got direct angelic protection because of the aforementioned "Fist of God" thing. As of the latest book, Ghost Story, the next oldest kid is a Badass Normal who holds his own in a knife-fight against an older, more experienced and super-powered opponent thanks to training from his parents. And surely there's more to come...
And that's not even going into what we know about Harry's family. We have a Badass Longcoat wizard who throws around Hellfire and Soulfire on occasion, summoned a zombie T-Rex, has won the loyalty of a magical prison designed specifically to cage the world's most powerful Eldritch Abominations, and is now the Knight Of Winter. Oh, and if you harm his daughter, he will exterminate your entire species. He demonstrated on the Red Court Of Vampires. His mom was an even more badass wizard who flouted the White Council's rules and got away with it. She got it from her father, Ebenezar McCoy, who is now regarded as one of the seven most powerful wizards in the world and is the only member of the White Council allowed to break the Laws of Magic. And then there's Thomas, Harry's long-lost half-brother, White Court vampire, and generally pretty awesome. Not to mention his daughter, who just might have killed the monster under her bed at around 10 years old. Better hope he doesn't have any more family hanging around, or the Black Council is going to be crushed, fast.
Elaine Mallory (technically Harry's sister since they were both adopted by Justin DuMorne) is also a badass wizard. Magically, she's strong enough to be on the White Council and has a lot of the same intensive training that Harry has. What she lacks in power compared to Harry, she more than makes up for in control and finesse. Just don't think about the part where she's also Harry's former lover.
Harry's faerie godmother is the Leanansidhe (goes by "Lea" in a pinch). In the Winter Court, she's second in power only to Queen Mab herself.
Even Harry's pets are badass. Mouse is a huge doglike sapient magical being that even members of the White Council respect. Mister is an apparently ordinary (if huge) housecat that somehow manages to cow Mouse. And is also the only thing Harry has ever run across that looks exactly the same under the Sight as it does to normal vision.
A Harvest of War has several pairs of relations kicking arse together: Tadhg and Wild Rhona (father and daughter) with Siegbert as a distant relation, Guinevere and Rhona Thyll (cousins), Aed and Medb Bors (brother and sister; their parents are also Retired Badass), the Mortimers (uncle and nephew).
In the Star Wars Legends continuity, the Solo-Skywalker clan. It got to be so obvious than when Jacen Solo became a Sith, his mentor advised him to divide them first, as when they work together they frequently prove to be unstoppable. It still didn't work: his sister, Jaina, working in tandem with Luke, is the one to finish him off.
Taken Up to Eleven if you include the Legacy era family ties. The Skywalker/Solo's family tree includes the Fels (meaning the Antilles, by extension), the Yage family via Morrigan Corde, and the Vos Clan via Rawk. Although they probably won't be on good terms, the Khai family (Fate of the Jedi) will likely come into the mix as well. By the Legacy Era, the Grandmaster of the Jedi Order (Kol Skywalker) and the Emperor of the New Galactic Empire (Roan Fel) are both direct descendants of Anakin Skywalker; the Skywalker-Solo clan is essentially holding the whole Galaxy together.
In-universe, Mandalorians invoke this Trope. They view all who follow their code as kin in one big, war-mongering family. Part of that involves marrying a fellow warrior and raising the next generation of Mandalorian warriors (with the father doing the bulk of it. One of their nastiest insults translates to "deadbeat dad"). If your spouse is of the same sex, different species, or infertile? Well, the galaxy has no shortage or orphans and parents who forfeit the honor - go out and adopt!
In Christopher Stasheff's Warlock of Gramarye series, Rod and Gwen Gallowglass and their four kids are, one and all, in possession of kickass Psychic Powers. Taking on the bad guys is nearly always a family affair.
Oh, very much one of Heinlein's favorite tropes. Consider the family in Friday, where a guy who pilots intercontinental suborbital flights is the underachiever. It gets to the point where Manuel O'Kelly Davis is considered to be the closest thing to an Idiot Protagonist in Heinlein's works: poor dumb Manny was an engineer who discovered (or even helped create) the first artificial intelligence in human history, as well as one of the leaders of a successful war of independence against an enemy several thousand times the size of his nation, but it's not like he was one of Heinlein's more competent heroes...
Manny has no fewer than seven artificial arms, only one of which is intended for use at social functions. The man can build practically anything once you show him the diagrams, and was the only competent computer engineer in the moon. Oh, and he could also run a farm and raise a family. And he was a miner before he lost his arm. And he was a judge for a while. And went to college on Earth. And was the entire government of Luna and sole architect of its foreign policy in the last days of the revolution. And how does Manny get included in this? Because he was one of the four leaders of the revolution, but half of his co-husbands and wives were the next tier down.
John Ringo apparently thinks highly of this trope:
The O'Neals in the Legacy of the Aldenata, whether related by blood or marriage (but more so the former), are so badass that even their pre-teen daughters are able to successfully play "tag" with invading Posleen forces.
The Keldara, from his Paladin of Shadows series (second book onwards) collectively make up a badass clan. They're all descendents of the Varangian Guard, Norsemen imported by the Byzantine Empire as guards for the Emperor.
The MacClintocks from his and David Weber's Prince Roger series, who founded an interstellar empire from the ground up, the hard way. When one character tries to describe the badassedness of the titular prince but fails to find the words, the commanding officer of the Badass Crew that are to serve as his bodyguards suggests "just say a MacClintock".
From Black Tide Rising there's the protagonist family. Dad is a former special forces soldier, both daughters (particularly the younger one, Faith) mercilessly slaughter entire herds of zombies, and mom is an engineer that keeps things working in spite of resource limitations imposed by the setting even if she doesn't herself participate in zombie slaughtering.
In the Amelia Peabody mysteries, the Peabody-Emerson family consists of: Badass Archaeologist Radcliff Emerson; his Action Mom wife, Amelia Peabody Emerson, for whom a parasol is a deadly weapon; their son Ramses who reduces even them to quivering terror; foster-child and later daughter-in-law Nefret, who wields a mean knife; and Uncle Sethos, the former Master Criminal! Throw in ferocious Arab in-laws, a Battle Butler and household staff to match and you have a crew feared by enemies of knowledge and justice everywhere.
Twilight's Cullen coven. A family of extremely sexy vampires that includes a mind-reader, a psychic, and an emotional sonar. Those that aren't gifted with extra powers are ALL Badass Normals. And they're exceptionally rich. Yeah, they're badass, all right. Jasper could manipulate people's emotions, Edward could delve into the deepest secrets of anyone's mind (save Bella), and Alice can see the future (not to mention all the others). They press in on the enemy from all sides.
Carlisle compassion and Esme's love is the glue that keep the family together and Bella completed the family power's vault when she married Edward, with a powerful shield that can protect them all from mind based powers.
The Oggs. Usually they're fighting each other, but piss any Ogg off and the rest of the Oggs will come after you too. And there are a hell of a lot of Oggs, including one witch and several Badass Normals.
Judging by Thud!, the Vimeses are on the way as well.
And if/when Carrot and Angua have cu- bab- whatevers, (of which there will be several) AM will have its own royal werewolf family, raised as dwarfs... Run now.
D'reg tribes take this Up to Eleven. Not only will men attack, so will women, children and pets.
The Edge Chronicles has The Verginix family. At least three of the family's members have been sky pirate captains, and one of them, Rook Barkwater, ends up as an equally badass warrior.
The family of sorcerers in The Belgariad. Belgarion gets to keep the MacGuffin on the pommel of his sword, Polgara combines extreme Mama Bear tendencies with some Sociopathic Hero traits, Belgarath is the most powerful man in the world and is described as being able to rip the tops off of mountains if he really wanted to, Durnik comes back from the dead and sends a Demon Lord back to the underworld by relentlessly pummeling him with a hammer...and that doesn't even start in on the rest of the disciples of Aldur.
The Zilwicki family from the Honor Harrington universe by David Weber. Mother Helen took out a Peep taskforce using only a couple of smallerships, dying in the process, to save the unarmed convoy her husband and daughter were on; for it, she was awarded Manticore's highest decoration for valor. Father Anton is a champion wrestler, expert hacker, and master spy. Daughter Helen is a martial arts expert who escaped from super-soldiers and killed three men with her bare hands when she was only 14 years old. Stepmom Cathy Montaigne is an incredibly wealthy noblewoman and House of Commons politician once she resigns the title over a matter of principle; she helps finance ex-slave terrorists in their war against the slavers and is THE galactic expert on slavery. Adopted daughter Berry managed to talk down a planet of revolting slaves and was made their Queen. Adopted son Lars is supposed to be following in Anton's footsteps. And that doesn't even begin to count family friends Master Tye (one of the greatest martial artists in the galaxy), Jeremy X (ruthless terrorist and firearms master), Thandi Palane (the soldier who super-soldiers are afraid of), and Victor Cachat ( Thandi's boyfriend and Haven's hatchet-man), all of whom are incredibly badass in their own special, terrifying ways.
The Harringtons themselves. Honor Harrington is a renowned military commander and lethal in hand-to-hand combat. Her father, Alfred, is a merciless killing machine of a Marine who was so good at it, he terrified himself and switched to medicine. Her uncle, a former Beowulf special operations soldier, was also a merciless killing machine and ordered assassinations of enemies just to make a point about messing with his family. Her husband, himself, was considered to be one of the greatest military commanders Manticore has ever produced.
Again by David Weber, the DeVries family in In Fury Born. Between the retired marine and his Super Soldier granddaughter who's Badass even by Super Soldier standards, they constitute the only family in the Empire to have two holders of its highest military honor at the same time. The pirate's field commander would later state that if he'd known the DeVries family lived on Mathison's world, he'd have bombed their home from orbit. And it would have been a sensible decision given what had happened to the entire platoon he had sent to raid their home instead. Between those two and Alicia's diplomat father, they took out all of them, despite the fact that they started the fight with two knives and a pair of hunting rifles.
Vorkosigan Saga's titular family; all four generations of the it. (Granted, Miles' and Ekaterin's kids just came out of the replicator, but one can safely assume they'll be badasses.)
At the end of The Saga of Darren Shan, it is revealed that Steve and Darren are brothers and Mr.Tiny's sons. Badass family that hates eachother.
The Butlers of Artemis Fowl have a long and storied history. There's a reason they named the word "butler" after them. Most notable are Juliet and the current Butler, Domovoi. He's usually just called Butler.
Also the Fowls themselves, although not so much physically. Two criminal geniuses (Artemis and his dad) and Angeline, though she gets less chance to show it, is hardly a slouch either.
No matter how big and tough you are, even if you're a terrifying demon from another plane of existence, it's a very bad idea to mess with anyone named Borenson.
Notably, based on the genealogical tables, every single Man and Elf Badass Family is related by marriage, and it all comes down to a point in Aragorn and Arwen, whose children have entirely too much to live up to, being the descendants of every hero the world has known except the hobbits and dwarves.
We could just say "Anyone descended from Beren and Lúthien" and leave it at that.
For the dwarves, the line of Durin definitely qualifies. Kings Thror, Thrain, Thorin and Dain all descend from this line, as does most of Thorin's company- Fili, Kili, Dwalin, Balin, Oin and Gloin are all legitimite members, whilst (in the films at least) it's implied that Dori, Nori and Ori are related on the wrong side of the sheets. And, of course, Gimli is a member of the line of Durin as well.
Also the house of Eorl, Rohan's royal line. Theoden, Eowyn and Eomer all kick many kinds of ass on the battlefield.
Tamora Pierce is the queen of this trope. Most Tortallan characters have, upon conclusion of their, moved on to found Badass Families if they weren't a part of one already. They include:
The Conté house, who aside from being the Royal Family are perhaps the coolest royal family ever. Quote from memory - "Next time you have to go out and chase down bandits, change out of your nice ballgown first, dear?" And, uh, yeah.
The Mindelan family, who are like the Weasley clan but with more daughters and cool in-laws and important political figures and Lady Knights.
Large parts of the cast also can be clumped together into several different overlapping sets of True Companions.
Briar, Sandry, Tris, and Daja of her Circleverse are four great mages soul-bound to each other, possibly the strongest mage team in the world, and see each other as siblings. And their foster mothers? Great mages. Their teacher/foster father? The most famous sight mage in the world. Their family friend? Great mage. Sandry's uncle? A badass pirate-fighting duke.
Most of their own students are well on their way to badassery themselves. Evumeimei (or Evvy), Briar's stone mage student, has already managed to communicate with fire spirits and save an island from destruction through volcanic eruption.
Eragon, who is a dragon rider who fights off a Shade in (mostly) single combat, kills thousands of men at a time, and can kill with one of 12 words. Also, his new sword is magically tuned to burst into flame whenever he damn well feels.
Roran, his cousin, who embodies the Determinator and Badass Normal tropes. He is a normal man, but he led a farming village on an epic quest to Surda, killed two immensely powerful magicians, killed 193 men in a house-sized pile... it goes on.
Selena, Eragon's mother. How awesome is she? Took on twelve expert soldiers with no weapons, and only a healing spell at her disposal. She healed them of what drove them to kill (anger, hate, fear) and then slit their throats with their own daggers.
Murtagh, Eragon's half-brother. Also a rider, and is actually a better sword-fighter than Eragon, as well as far more powerful. Personally hands Eragon's ass to him at the end of Eldest, and then goes on to hold his own against Eragon, Saphira, and thirteen elves at once in the next one.
Brom, Eragon's father. Killed 3 of the Forsworn personally, had another 4 or so poisoned, and defeated a Rider and Dragon without his own dragon, who had been killed. He is also notable for founding the Varden, the main rebellious organization in the series.
The Basheres in The Wheel of Time. Davram, one of the Five Great Captains, Faile, the politically savvy knife-wielding wench. Finally Faile's husband, Perrin Aybara, the hulking, axe/hammer-wielding, 'Wolf King' blacksmith. Her mother, Deira walks into her tent, finds two bad guys in it who attack her, to paraphrase: "...So of course I stabbed one and hit the other with a chair."
Nearly everyone in Percy Jackson and the Olympians. Every single one of the demigods has Greek god parentage, which makes them related on technicality to everything and everyone in the Greek Parthenon, and then Percy and Annabeth are shown to have some pretty badass parents, what with Annabeth's dad flying a plane THROUGH THE MIST (both kinds) AND DISTRACTING ATLAS, and Percy's mom and second step-dad defeating several monsters blind.
How did Annabeth's father create such a distraction? He slaughtered dozens of monsters in the Titan army with only a plane and gun he made in his garage.
Not to mention Reyna and her sister Hylla. They survived being kidnapped by pirates together. Now one is the teenage praetor of a Roman legion. The other is the queen of the Amazons. Both are unquestionably badass.
By the time of the later books, the Atreides have spread to much of humanity, including all of the Bene Gesserit (The Siona Gene, which makes someone invisible to seers), but those with stronger connections, such as Miles Teg, still stand out. Teg can accelerate his metabolism, and sense no-ships
The Varyl ilian in the One Rose Trilogy. A family group of eleven highly-trained warriors? They have magic that hasn't been seen in a thousand years? Yeah.=
The Sadiablo family of Black Jewels is a prime example. Family patriarch Saetan Daemon Sadiablo is the strongest male in the history of the Blood until his son Daemon comes along as well as the first Black Widow; he also ruled Hell while he was STILL ALIVE. His sons are a collection of the most terrifying, powerful, brutal, feared males the Blood have ever heard of. Oh, and his adopted daughter is Witch herself. That's not even considering the collection of nieces and nephews he picks up through his connection to Jaenelle.
The Wiggins of Ender's Game. The parents are already geniuses, and all of their children are badasses before the even hit their teens. Ender, the military genius who nearly wipes out a starfaring RACE, and Peter and Valentine, who start off with just a blog and eventually manage to rule the world. And if you include Jane as Ender's adoptive "daughter", you get a whole new class of badass.
Arutha and his family from The Riftwar Cycle. He took down Murmandamus, his wife lived with thieves for weeks to escape capture, his twin sons saved Kesh from itself, and his youngest son conquered new land for the Kingdom of the Isles. And if you add in his siblings, it gets even better: his brother Lyam becomes a great king, his half-brother Martin was raised by elves and is freaky good with a bow, and his sister Carline fights as well as a man in Magician''.
The Kholins from The Stormlight Archive are mostly pretty awesome, Dalinar's a Shardbearer at least until he gave them up and all around awesome fighter, Adolin is ALSO a Shardbearer and awesome duelist, Elhokar is the king and ALSO a Shardbearer, Jasnah is a renowned scholar and has badass innate Soulcasting powers, Navani is a brilliant engineer, and Renarin charged a massive monster of death at one point, despite being one of very few Non Action Guys in the book, Also Renarin now has Shardplate courtesy of Dalinar, awesomness is expected to be upcoming.
All of them except Navani have been confirmed via Word of Brandon to have the potential to become Knights Radiant.
And as of the second book, Shallan Davar, who is both a Lightweaver Radiant and a Shardbearer, is betrothed to Adolin and looking likely to make it a marriage soon. Dalinar has become a Bondsmith, an order of Radiant so powerful that no more than three ever existed at any one time, while Renarin has manifested the powers of a Truthwatcher and Adolin's dueling skills continue to rise.
As of the third book Shallan is officially married to Adolin and has taken several levels in badass, and there are signs that Adolin himself may be awakening the dead spren of his Shardblade, which could potentially result in him becoming an Edgedancer. Also Dalinar managed to flip off Odium, temporarily unite the three levels of reality, and bind a powerful evil spren.
The Kinnison family from E.E. "Doc" Smith's Lensman series.
Father Kimball Kinnison is the only human Lensman who has learned to use his psionic abilities without his Lens, and without his psychic powers can still defeat a dozen thugs at once.
His wife, Clarissa McDougal Kinnison, is at least as powerful as her husband, though she generally doesn't fight (there are two spectacular exceptions in the final novel). She's a nurse and sometimes an infiltrator, and the only woman ever to be made a Lensman.
Their children are even mightier, fully capable of coordinating and channelling a massed telepathic assault by a many million mind strong army upon a world of almost unkillable protean aliens. After the kids broke the world's primary mental defences. Alone. All this is justified in-universe in that they are the end result of a breeding programme stretching throughout the entire history of the human race, and their parents are the penultimates.
The Royal Family of Amber from The Chronicles of Amber by Roger Zelazny. The most murderin', schemin', backstabbin' bunch of Machiavellian bastards around! Hell on other people when they're not killing each other.
Tavi's extended family of Codex Alera. Tavi himself is crazy like a fox, his uncle is a potent earthcrafter and woodcrafter, his mother is usually just a healer, but when Tavi is threatened she does things like throw a shark onto the deck of a ship. Then there's Gaius Sextus, who needs no introduction. Then marriages start occurring. Amara is the fastest flyer in the realm, and a Fragile Speedster who's reasonably good with a sword. Araris Valerian is the best swordsman in Alera, and his little brother is up there. Kitai is a good deal stronger than she looks even before she gets furycrafting, and her dad is stronger than he looks as well, and he looks like he bench-presses refrigerators and is bonded to Walker.
The descendants of Bink in Xanth are all magicians, all slated to be Kings, and all have to go on adventures because something. The series gets pretty silly eventually, but for the first dozen books or so, the family is pretty legitimately awesome.
The Cthulhu Mythos has children of Idh-yaa, quasi-woman creature from Xoth - Cthylla, who is source of all legends about giant squids, Ythogtha, who has been bind by the Old Ones with seven chains and when first one broke, it caused entire continent of Mu to sink, and two other gods, Ghatanoth and Zoth-Ommog, who remains msytery, but possibly are pretty badass as well, considering who is all four's dad. You might have heard of him, he is quite famous. His name? Cthulhu.
Time Scout: Meet Kit Carson, his granddaughter Margo Smith, and her fiancé Malcolm Moore.
The Whistlers of A Brother's Price. The current generation are the grandchildren of a prince and about ten women who were soldiers-turned-thieves-turned-spies and passed down a lot of their learning. Captain Tern notes that the injured Princess Odelia is safer in the Whistler home than she would be at the local garrison. The whole family, even the small children and boys, have some degree of training.
The Redwall series has many badass families. First is Matthias's family, a mouse who beheaded a giant snake and killed a believed to be invincible Rat warlord Cluny. His wife singlehandedly brought down an entire siege attempt by Cluny albeit by accident. And their son Mattimeo barely doing any fighting himself, once being taken as a slave became a being of leadership and confidence towards the others.Then there is Luke and his son Martin both kickass fighters in their own rights, the latter who was revered so much as a hero, that he became practically a Saint which Mattimeo named his son after, who is a pretty awesome fighter as well. Luke even said he had a grandfather named Martin who implied was an epic warrior. And then there is the Reguba Clan, who are infamous in the land for producing generations of badass warriors. (Despite the Reguba Clan only appearing in one book) Also there is the Brocktree linage, an entire family of extremely powerful warriors.
The Yarikas in Rogue Sorcerer have a reputation for becoming masters of combat. Particularly impressive is Lyr Yarika, who has a penchant for handing other badasses their...ahem...asses.
In The Poster Children, the Underwoods, unsurprisingly. Corbin played the dark reflection to his friend's Captain Patriotic. His wife Amira was a chess prodigy and joined an intelligence agency before she reached double-digits. The first son Marshal was forced to run away and become a vigilante after killing the murderer of Matt, the second son. Ellie, the adopted daughter, spent her early years with them patching up Corbin and Marshal after nights of crimefighting. Mal, the youngest, scored perfectly at the end of his first block in a superhero school when his only actual power is a Healing Factor. Basically, they are not to be underestimated.
The Muriens. Earl Muriens is a Badass Normal with twenty years of successful campaigns against the Wild monsters and Outwaller tribes under his belt, and his wife is an an insanely powerful sorceress. Of their sons, Gabriel is a stellar tactician, mage and knight, Gavin started his career by killing a demon twice his size and Aneas is both a skilled sorcerer and a great fighter.
The Lachlan brothers. Thomas is a One-Man Army on a battlefield, Ranald is a Badass Normal knight and Hector, despite technically being a non-combatant, manages to take down over a dozen Wild Creaturs before he's killed.
Mother and son Tar and Lot are ancient dragons who both manage to fight the villain of the series one-on-one on even terms.
In the Enforcer series of Warhammer 40,000 novels, the protagonist, Shira Calpurnia, seems to be upholding the family business of Professional Badass. The Calpurnii are from Ultramar, homeworld of the Ultramarines, a famous chapter, even if not the biggest nor the most badass. Calpurnii are rogue traders, Imperial Guard officers, lord admirals, Arbites commanders - Shira had a great cousin who was an Ultramarine Terminator during the first Tyranid invasion. Shira herself is a lethal combatant in hand-to-hand or with a maul and shotgun, and proves repeatedly that solid fucking steel runs in her veins rather than blood. This is even brought up as a point in the story. Another arbiter notes that, by the standards of the Imperium as a whole, Calpurnia has a better pedigree and lineage than virtually all the nobles on Hydraphur.
Horus Heresy has the Emperor and his sons. The Emperor himself is a thirty-six-thousand-years-old psyker bordering between Humanoid Abomination and Physical God, who crafted the Imperium by creating a Badass Army and then leading it from the front and beating the galaxy into submission. To match this, each of his eighteen kids is a three-metres-tall One-Man Army capable of fighting faster than a human eye can follow and with mastery over nearly all weapons and military strategies known to mankind.
Dance of the Butterfly has two of these, and they are rivals, the Felcrafts and the Malkuths. Both are immensely wealthy and influential, and they also just happen to be part of a conspiracy to hide the existence of invading demons that they actively hunt.
My Vampire Older Sister and Zombie Little Sister has Satori and his titular stepsisters. Satori is a Guile Hero who managed to build an AI capable of simulating an entire city or hacking into security systems. Erika and Ayumi are the vampire and zombie, respectively, and are both Persons of Mass Destruction capable of infecting the population of an entire city (in the simulation by the aforementioned AI). And it's later revealed that their parents/step-parents are this as well. Taizou, Satori's father and the sisters' stepfather, is a researcher in the Bright Cross. Yurina, Taizou's second wife and the siblings' stepmother, is the Biblical Lilith, a demon lord capable of easily overpowering Erika and Ayumi simultaneously. Taori, Taizou's first wife and Satori's biological mother, was originally human but was later enhanced to the point of being able to fight Yurina head on.
Daniel Keys Moran's "Tales of the Continuing Time" has the Castanaveras clan, a family of genetically engineered people who are super-soldiers and/or telepaths. They are a family in the sense that they are all tweaked clones of Carl Castanaveras. Their capabilities so terrify the organization that created them that they are destroyed by a nuclear strike. Three of the family escape (Trent, Denice and David), and are the focus of the next several books.
The Periwinkle of the Ways family is made up entirely by powerful Magicals and Badass Normal people.
The Burdock family have a long history of powerful Magicals of the Dark.
The Poppys are the most magical beings in the world by the maternal side. They inherit magic itself.
Deeplight: Dotta Rigg's kids are routinely trained up as part of her smuggler crew. The Riggs are feared and respected around the island of Lady's Crave.
InCryptid has the Price family, in which every member is trained from a young age in combat, survival, stealth, and cryptozoology. Their Rite of Passage is to take whoever's just turned 18 blindfolded to an unfamiliar location in the wilderness, drop them off with no weapons, and see how long it takes for them to find their way back home.
The Prices used to be a Covenant family, and the remaining families in that organization have similar training for their children (though with the goal of exterminating cryptids, not studying and protecting them). When Dominic is introduced, his training allows him to go toe-to-toe with Verity.