Having a Superhero parent is like being Blessed with Suck. There's the bi-weekly kidnappings, frequent Parental Abandonment, being constantly lied to if your parent has a Secret Identity, being forced to lie to maintain your secret, and constant worry that your parent(s) or you will be killed by a vengeful supervillain. But look! You can fly!
Normally, heredity is a messy affair; it's often described as a game of chance. Thanks to Darwin, Mendel, Watson and Crick, it can be explained a good deal better, but much like A.I. Is a Crapshoot, what traits a child will inherit from each parent are mostly random. Not so with superpowers. Children of "supers" can have a limited number of things happen:
Develop identical powers to their parent(s).
Develop radically different (and usually insanely powerful) powers from the parent(s).
Super-power inheritance tends to happen more often than could be ascribed to chance; a non-powered child of even a hero and a normal person is an exception. Super-powers seem to be "more dominant than dominant".
If a parent's powers are caused by gene splicing, or from being born a mutant or part or full alien, then it gets interesting. Specific powers actually have a higher chance of not being inherited. In such cases, the child usually gets a completely different power, or at best one that's only tangentially related. This becomes much likelier if both parents have different powers. Only occasionally will they just have a combination of their parents' powers; this tends to happen if the parents' powers are very simple, or if the series was designed around the child, and the parents were brought in as part of the Back Story as a Secret Legacy. If this happens often enough, it may be revealed that all the powers of that family are just different expressions of the same gene as a Meta Origin.
If only one parent has powers, however, the child's powers are much more likely to be a straight copy of those, though often at a higher level. This may encourage the writers to give that power its own Meta Origin.
See also Superior Successor, Lamarck Was Right, Genetic Memory, Magic Genetics, Bio-Augmentation. Compare Muggle Born of Mages. Settings that avert or minimize this trope may use Randomly Gifted instead.
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Dragon Ball Z repeatedly shows that hybrids of humans and super-powerful aliens produce insanely powerful offspring. Lampshaded by Vegeta, when he notes that he trained intensely to unlock his Super form, while his hybrid kid can do it for fun. If a child is conceived after the father has unlocked said Super form, that child will be able to do so with essentially no effort, in a case of Lamarck Was Right. If the child was born beforehand, it's quite a bit more difficult. They're crazy powerful regardless, though. The only real exception to this out of ALL the half-saiyan children is Vegeta's daughter Bra, who he apparently chooses to dote on rather than train.
Before any of that, this trope is Played for Drama in the Cell saga, where the Big Bad was created from the genes of most of the heroes. This gave him all of their strengths and their deadliest techniques.
In the future, descendants of Vegeta and Goku don't even realize the significance of their Super forms other than noting their hair turns yellow.
The author admitted he had no idea what to do with or even how to handle a female Super-Saiyan so he just ignored Bra.
In Hunter × Hunter, insane Nen-potential seems inherited just like insane physical potential.
Tenchi Masaki of Tenchi Muyo! is slightly over one quarter Juraian (his father happens to be a descendant of his maternal grandfather). Juraian's are an alien race with a tendency to develop Jedi-like powers with training (the royal family being stronger as well). He's also the most powerful "Juraian" in existence; capable of manifesting three "lighthawk wings", one of the most powerful defensive/offensive attacks known. A typical Juraian space ship is capable of manifesting only one.
OVA Tenchi is most likely disqualified from this as he's the avatar of his dimension's god. However, the one from Tenchi Universe more than qualifies as it's said that his own Juraian power was passed down from his mother, who was pretty damn powerful in her own right.
In Ranma ˝, the Musk Dynasty bore offspring through wild, powerful animals that had been thrown into the Spring of Drowned Girl, thus turning them into women. Their children would then inherit traits exhibited by, or closely related to, their mothers' natural form. Hence, Mint's superhuman scent, hearing, and speed (born from a wolf); Lime's grotesquely overpowered physical strength (born from a tiger); and Herb's ability to fly and discharge his ki in devastating streams (born from a dragon). One episode of the anime hinted that children of a cursed parent will inherit that parent's curse- but that episode was all one of Ranma's nightmares, so it's not canon.
A number of ninja clans in Naruto have special genetic powers referred to as "kekkei genkai", or "bloodline limit". These include eyes that can copy others' abilities, being able to manipulate and regrow your own bones, any Elemental Powers which are formed by combining any two of the basic five elemental affinities (for example, Water + Wind = Ice), etc. There are also abilities that seem like this, but are actually just well-kept clan secrets, such as the Nara clan's ability to manipulate shadows.
However, genetic powers aren't always passed down. The best example of this is the First Hokage's wood release, which was entirely unique to his DNA, with none of his descendents inheriting it. Another example would be the Third and Fourth Kazekages, who seem to be the only members of their families capable of using magnetism.
Quincy powers are hereditary, leading to an clan-wide obsession with bloodlines.
Ichigo and Karin can see ghosts, Yuzu can see faint outlines of them, and Ichigo eventually became a Shinigami with an extremely high amount of spirit energy. Why? Their father Isshin is a retired Shinigami, and has all the same powers Ichigo does, at a Captain's class. Ichigo also inherits hollow and Quincy powers from his mother's side that make his attempts to master his abilities very complicated.
Weapons in Soul Eater come about in this way, thanks to the 'bloodline' of the original experiments. It's possible for a weapon to show up in a family that hadn't had one for a very long time, which we see is what happened with Soul Eater himself. For some reason, the Nakatsukasas had come to expect that the eldest child would inherit the Morph Weapon abilities. When this did not happen, things did not end well. Kid falls definitely into the 'will eventually inherit' category, as BREW so helpfully showed off.
While Tiger & Bunny's Word of God says that NEXT abilities aren't genetic, it's certainly telling that the two superheroes who were fathers (Wild Tiger and Mr. Legend) ended up having superpowered children (Kaede and Yuri Petrov).
Subverted in +Anima. People with Anima power are believed to have Kim-un-Kur blood in their veins. In reality, children gain the ability to turn into animals they see during their near-death experiences.
The children of Fantastic Four members Reed and Susan Richards show two variations. Their daughter, Valeria, has been shown in a future timeline to have a more advanced version of Susan's invisibility powers (other alternate Valerias have been shown with a variety of powers), whereas their son Franklin is sort of... intermittently omnipotent.
Valeria is currently a super-genius; three years old already Reed-class. Franklin is currently depowered after the last time he pushed his omnipotence into overdrive. At his maximum, he is potentially one of the most powerful beings in the universe, to the point that characters who can make Galactus sit up and beg were afraid of him for a while. When he has powers, there's usually a Restraining Bolt (imposed by him or others depending on the timeline) on them that limits him to helpful but not god-tier psychic abilities.
Gina Diggers is a definite type 5. Despite being the only daughter of Earth's most powerful aura mage and Jade's greatest warrior she has absolutely no talent for magic or fighting whatsoever.
Descendants of the Flashes universally inherit Super Speed; The DCU's "meta-gene" was called in to explain this. Many other DC characters avoid this trope by having their successors or apprentices come with their own origins.
Another example of a superpowered lineage could be found in the DCU Manhunter series. Kate comes from a long line of metahumans. Her great grandfather Hugo Danner, grandfather Arnold "Iron" Munroe and father Walter Pratt were all superhuman. While Kate herself is not fully-superhuman, she is unusually strong and tough and it is implied that she is a borderline metahuman. Her son Ramsey inherits powers that easily exceed any of his ancestors. He is also an extremely rare fifth generation metahuman.
The main characters of Runaways tend to have superpowers corresponding to those of their parents. Many of these "powers" are magical or technological gifts.
In Runaways, Molly Hayes initially appears to have not gotten the mutant gene despite her parents both having it. Early on in the story however, she is discovered to have super strength (while both parents had mind controlling powers, and her strength turns out to be psionic in nature). Karolina has exactly the same alien powers as her parents which her mother points out means that none of them can hurt each other. Chase is the son of two brilliant Mad ScientistGadgeteer Genius types, but his abilities run more to minor cleverness, street smarts and punching things. Gert has a pair of travelling also mad scientists (but more biology based) for parents and though she is gifted with there intelligence, her power is actually something they engineered for her - being psychically linked with a bio-engineered Deinonychus (think Jurassic Park Raptor).
Wolverine's recent Retcon backstory posits that he is descended from two powered families, one with bone claws and one with a Healing Factor. Nightcrawler is likewise (supposedly) the child of an ages-old mutant clan with interdimensional powers, and Angel is implied to be from an angel-like mutant bloodline as well.
Clan Akkaba are descendants of Apocalypse, and each member has inherited variations on his powers. The greater families, including the Slades, have a weaker version of Apocalypse's shape-shifting and longevity, and a minority also possess his grey skin. The 'Lesser' members have different and unique powers, such as Jack Starsmore, who can instead breathe fire. Rarely shapeshifting members randomly gain additional mutations, such as Frederick Slade, who has pink hair, solid green eyes and teleportation, shared with his descendant Blink. Chamber's powers as a psychic furnace are very different to his ancestors Jack Starsmore and Apocalypse.
In Young Avengers, on the other hand, the "brothers" Tommy and Billy apparently got the same powers as their "mother" Wanda ( it's complicated) and uncle Quicksilver - Tommy has superhuman speed and Billy can manipulate reality by expressing a desire for it. Any powers from their "father" the Vision seem to be nonexistent, possibly because Wanda "gave birth" to them herself, though given the incestuous overtones there've been between her and Pietro this leads to some Unfortunate Implications. Cassie Lang shares the same growth powers as her father Scott, however this was from her stealing Pym particles and not inheritance (her father's superpowers weren't genetic). While Patriot has no powers from birth, he does get superhuman strength from his grandfather (formerly one of the Captain Americas) via blood transfusion. FF foe the Wizard is a Mad Scientist with no powers, but being around gravity-manipulating technology most of his life lets him have a daughter who controls gravity innately.
Quicksilver and the Inhuman princess Crystal's daughter Luna subverts this. The X-factor and Inhuman genes cancel each other out, leaving Luna an effectively baseline human. Her dad, driven crazy (well, crazier) by the loss of his powers thanks to M-day, exposed her to a heavy dose of Terrigen Mist to correct this "error". Thankfully, it worked. Luna survived (though she developed a bit of an addiction to the Mist) and gained empath powers.
One of the consequences of M-day was that mutants could no longer have mutant offspring. They could still have children, but the children would be baseline humans.
A possible future introduced Ruby Summers, daughter of Cyclops and Emma Frost. She has her father's eye beams and has also inherited her mother's "secondary mutation", only instead of diamond she turns to ruby, reflecting her father's ruby-quartz visor.
In stark contrast to Graydon Creed mentioned above, Mystique's and Wolverine's future son Raze has both of his parents' power-sets.
In Rising Stars, it's explicitly stated that the children of the Specials inherit no powers.
The WildC.A.T.s are all descendants of the Kherubim and/or the Daemonites, super-powered alien races, and inherit their powers— since both races have a vast array of potential powers, the humans usually only get a random fraction of them.
Gen13 and their Evil Counterpart team DV8 inherit powers from the genetic Super Soldier project that produced Team 7 and other gen-actives. Generally, these powers have nothing to do with their parents' powers (except the time Burnout inherited his father's Mind Control powers for about a week).
Zenith is a slight subversion; he does get his parents' powers, just not all of them, and they don't work all the time.
Marvel's Eternals avert this; they can breed with mortals, but the kids are just normal humans. This plays a part in Ikaris' tragic Back Story (here's a hint; he took the name Ikaris in honor of his late son).
Eternals breeding with Eternals rarely produces offspring, but they are full Eternals—except for the Titanians, who originally only had half the power of the Earth Eternals, and whose current population are descended from both sides of the "family", resulting in wildly varying power levels and longevity. Then there's the Ritter twins, children of an Eternal and a Deviant (another offshoot of humanity with constant mutations); they appear as normal humans but can Fusion Dance into either one or two Eternal-powered beings, Depending on the Writer.
Lampshaded in Invincible. Invincible's super-powered alien dad explicitly has genes that beat up and take over the genes of whatever he mates with, creating offspring that are almost identical to himself, powers included. Case in point, he also mates with a humanoid praying mantis girl and produces a child who looks perfectly human except for his purple skin.
The Man of Steel has no canonical descendants, though the issue has been explored in many "imaginary" stories. Classically his children with a human wife have all his powers at half power level. The Generations storyline affirms this with halving occurring with each successive generation. One Elseworlds had one of Kal-El's Ancestors land on Earth and take over, with each successive generation being less powerful to the point that Kal-El himself had no powers and his father was barely superhuman.
More recent examples of his offspring include a child of Superman and Wonder Woman who ended up being an alternate version of the Phantom Stranger. In DC One Million, his offspring apparently retain their powers through successive generations and gain new ones by intermarrying with various species including a 5th dimensional being, forming a Superman Dynasty. Superman himself returns in this timeline after hundreds of thousands of years transformed by exotic energies and gaining the ability to bestow additional powers on his offspring. The Superman of the 853rd century, a direct descendant of Superman, is like our Superman on steroids.
The aforementioned Generations storyline has an odd instance of a type 5 in Superman's son Joel Kent who would have had his powers had he not been exposed to Gold Kryptonite in the womb. Much to Joel's bitterness and dismay, his younger sister was not exposed and ended up a type 1.
Hinted at in another 'maybe' story. Superman officially died ten years before the story begins. While a reporter is talking to a now-married Lois Lane for an anniversary article on events, her baby boy is seen crawling around. After her husband comes home, the baby is playing by the fireplace with a piece of coal. The next frame shows the baby in the same place playing with a diamond. No, they did not find a body ten years before.
The Hulk's kids are an interesting case. His son, Skaar, inherited both his parents' power sets - giving him the power to control the earth in addition to the Hulk's powers. His twin brother Hiro-Kala only got the tectonic powers. His daughter Lyra, created via genetic engineering, got only a measure of the Hulk's superstrength; instead, she developed the ability to attune herself to gamma radiation - in combat, she can almost always position herself exactly where she needs to be. Unfortunately, thanks to deliberate tampering in her creation, the angrier Lyra gets, the weaker she gets.
And it turns out all Gamma mutates are descended from a single common ancestor who had the latent genetic trigger that causes gamma radiation to grant superpowers as opposed to nasty radiation sickness.
Not all; Bruce Banner's mentor, Professor Gregory Crawford, who discovered said genetic trigger while examining Bruce's blood, found a way to copy it through genetic manipulation, which he used to turn himself into the Gamma mutate Ravage. It's also suggested that the Red Hulk and Red She-Hulk didn't have the genetic marker themselves, and were only created and stabilized after significant genetic modification.
Betty Ross (Red She-Hulk) has the genetic marker, as Modok had previously turned her into the gamma-mutate the Harpy to use her against the classic Green Hulk (her Red She-Hulk status being a result of combined gamma and cosmic ray exposure).
In the case of The Savage Dragon, the main character's son Malcolm directly inherited full-power versions of both parents' powers, which isn't so surprising if you know that Dragon's powers run in his family's dynasty. His mother's electrical powers were given to her later in life, so they must have caused genetic changes, thanks to Golden Age villain Doctor Nirvana's experiment.
This series has a ton of examples of this trope, as it's been running in real-time for nearly twenty years, leading to many second-generation characters appearing constantly.
Planetary: It is explained Century Babies all have extended lifespans in addition to their abilities. Their children will also inherit the extended lifespans, along with abilities of their own, as evidenced by Jakita Wagner and Anna Hark, but not William Leather(whose mother cheated on his father, a Century Baby).
When a character in the Lensman series has the last name "Kinnison", you can be sure they're going to kick ass. They may die in the process, but ass will be kicked in the meantime. Kimball Kinnison (the hero of Grey Lensman and Second-Stage Lensmen) eventually marries Clarissa MacDougall, a descendant of Virgil Samms, the eponymous First Lensman. Their kids are the Children of the Lens, and they're explicitly stated to be the most powerful minds in the Galaxy, exceeding even the Arisians who created the lenses. To give just one example, while son Christopher is given a Lens, his four sisters are not ... instead, they realize they might be useful occasionally, create them out of thin air using sheer mind power, and then dissolve them again the same way until they're needed.
Spider-Girl: May "May Day" Parker is the daughter of Spider-Man Peter Parker and not only did she inherit his powers (that didn't manifest till her teens) but also his sense of humor, fight banter, and his academic skills. However she's not exactly like him as she got her mother's good looks and social skills.
In The Incredibles it explains how a super-strong guy and a stretching woman give birth to a super-fast boy, a girl with invisibility powers, and a shapeshifter.
A type 2 in Film/Looper, though not exactly "super powerful" in the beginning. The resident Chekhov's Skill in the film, the mutant's telekinesis, is fairly common and doesn't really impress anyone. However, Sara has a notably stronger version of it, and her Cid - being her child and that of another mutant - has that power turned Up to Eleven.
In X2: X-Men United; the mutant gene is said to be passed down from the father (but not explicitly stated to be located on the Y chromosome). Though given the tension of the scene, it seems likely that Pyro was simply exploiting Mr. Drake's ignorance to make him squirm.
Sky High goes with the fourth option twice. After spending a long while thinking he would never develop powers, the main character inherits his father's Super Strength and his mother's Flight powers separately (both were Die or Fly situations, the second a Suicidal Gotcha using flight). The bus driver, and only other person on record to have super parents and not get powers, just exposed himself to toxic waste and grows 50 feet tall on demand. Nurse Spex also states that sometimes powers just aren't passed on at all.
Necessary Evil seems to be reaching for both 4 and 5, with the brothers.
The Disney movie Up, Up and Away involves a boy named Scott whose parents are Bronze Eagle and Warrior Woman. Bronze Eagle can fly, and Warrior Woman has super-strength as well as a super-fast motorcycle. His big brother, Silver Charge, has super-speed and electrical manipulation. His little sister has x-ray vision and Eye Beams. Even his grandparents on his father's side have super-strength/flight (grandfather, Steel Condor) and Voluntary Shapeshifting (grandmother, Informed Ability). Scott's problem is that he's quickly approaching his 14th Birthday, and he has yet to develop any ability. 14 is the cut-off for a super. If he doesn't get an ability by that time, than he's just a Muggle. To that end, he decides to fake having super-strength (by rigging a door to fly off its hinges) and flight (by throwing a ball at a tree and hiding). In the end, though, it's his normalcy that ends up saving the day.
In Stephen King's Firestarter, the young female protagonist inherits powers from both of her parents, squared - despite the fact that their superpowers were caused by an experimental drug, not genetic tinkering.
Inverted in the Wild Cards anthology series. Superpowers are caused by the Wild Card virus, which can be passed on by either parent, and is always passed on if both parents have it. However, only 1% of infected people become super powered "aces," regardless of how they were infected. This means the child of two aces is 9% likely to become a deformed mutant, and 90% likely to die a horrible death.
One ace character must break off his engagement to his childhood sweetheart when he finds out she has the virus too— and he can't even tell her why.
There is one case of an ace having a daughter with identical powers, but this is explained by saying he psychically manipulated her genetic structure in the womb. If there was a trope for Suspiciously Specific Superpowers, that guy would be the Trope Maker.
The Psi Lords of Takis have inheritable powers, which is to be expected since they are the products of a Super Breeding Program specifically geared towards perpetuating their telepathic abilities into successive generations. The traits appear to be dominant, but can still breed out over generations. For example, Dr. Tachyon's grandson (by way of ordinary humans) Blaise exhibited stronger-than-normal mind control, but no other telepathic abilities, suggesting that Psi Lord powers are not all derived from a single gene.
In Harry Potter, some wizards have two wizard parents, some have only one wizard parent, and some are Muggle-born. In this case, magical ability might be explained as a dominant mutation that often occurs spontaneously...if anyone ever bothered making Harry Potter sound logical.
This was explained in The Tales of Beedle the Bard: so-called "Muggle-borns" will actually have one or more wizarding ancestors somewhere in the family tree.
This makes it look more like a recessive trait, given the fact that Muggle-borns are common, and Squibs (nonmagical children of magical parents) are extremely rare (of the Loads and Loads of Characters in the books, only 2 are squibs). That doesn't explain why almost all kids of a witch/wizard and a Muggle are magical, however.
A version occurs in one of the Serendipity books when a pegasus mare mates with a mortal stallion. When she turns out pregnant, a wise old mare explains that the child could be born with either legacy. Turns out he's born with tiny, tiny wings, obviously unable to let him fly - but still the mother thinks perhaps they'll grow. However, by the time she must leave (for if she stays, she too will lose the ability to fly), the wings are as small as ever. She wings away into the clouds, trying to ignore the cries of her terrified child. But the series being full of magic and generally using happy endings (even with bittersweet overtones), the foal comes up after her, in those few minutes having sprouted (through willpower alone) wings large enough to carry him.
It's indicated in Damia's Children that more powerful Talents have more powerful children -usually-not-always. Sometimes a powerful and a 'weak' talent can produce some truly remarkable results.
In the Young Wizards series, wizardry is known to run in families, though it probably has more to do with inherited traits The Powers think make a good wizard more than any "wizardry gene" since the power has to be offered by them and accepted through the Wizards Oath. In Nita's family there's Dariane, her aunt and offscreen, her great-grandmother, all on her father's side.
Both the ability to manifest Deryni powers and the Haldane potential (apparently a variant) are transmitted genetically; the trait is dominant, so only one parent needs to have the trait for an offspring to inherit it. Thus, so-called "half-breeds" are just as powerful as full-blooded Deryni. Deryni generally need to be taught to use their powers; carriers of the Haldane potential need no training, but must have the potential triggered by a outside action. This is usually done in a ritual, the specifics of which vary slightly from one generation to the next; certain heirloom objects are used, and new ones may be added.
It's kind of annoying how each new child of the Skywalker line is touted as having the Strongest Potential Ever. In I, Jedi Corran learns that the creation of illusions and permutations of the Jedi Mind Trick, ability to absorb and convert or channel energy, and the inability to use telekinesis unless currently channeling energy are all Halcyon family traits, and his grandfather was a Halcyon. Over time he manifests each trait. Jedi who are not Skywalker-descended can have non-Jedi siblings and relatives whose weak Force-Sensitivity manifests as things such as a bit of "luck" and accurate hunches.
It seems like that if a Force-Sensitive is cloned, the clones will themselves be Force-Sensitive, as shown with Jorus C'baoth and Joruus C'baoth. Though the clone's origins are mysterious enough that it is entirely possible Palpatine created and discarded dozens of C'baoth clones before getting one with the original's power. The clone also makes a clone of Luke, but the Luke clone might not have been a Force user.
When Vader clones Starkiller, the clone retains the original's extremely strong abilities (the original could pull a Star Destroyer from the sky, while the clone can disintegrate anyone around him with a Force wave and super-charge a ship turret to blow up a Star Destroyer). Additionally, Vader's attempts resulted in dozens of failed clones who still exhibit powerful abilities.
One of the drawbacks of cloning Force Users though (therefore why neither the Jedi nor the Sith do so to shore up their numbers) is that cloned Force Users tend to be mentally unstable.
Several of the creators of the Old Kingdom invested their power in specific bloodlines. As such, the Abhorsens, royals, and Clayr all tend to manifest the appropriate powers as needed.
In The Dresden Files, magic runs in families, usually matrilinearly. This is part of a villain's plot in White Night, when some of the White Court start killing off female magical practitioners too weak for the White Council to notice, on the logic that this will interfere with future generations of wizards and they can afford to wait.
Complicated by the fact that sufficiently skilled crafters can pass control of their pokemon on or before death, giving multiple meanings to "inherit their power".
In The Elvenbane, powerful elvish spellcasters produce children who're powerful, weak casters produce weak children, and intermarriage between strong and weak produces a child of intermediate power. At least in the first book, it's never explained where powerful spellcasters came from in the first place, but their attempts to stay powerful through the generations have led to severe inbreeding. Human spellcasting is also inherited, but in defiance of the trope it's an indirect and imprecise pattern. note (Elves and humans aren't even from the same world, so the implication is that human magical power is determined through standard genetics, with multiple genes influencing power levels, and elvish magical power is determined through something else entirely. Then again, elves and humans can interbreed, which shouldn't be possible for two species with very different genes. Then again again, it's a fantasy story—what do you expect?)
Lampshaded in a narrative comment on how the elves don't really understand human inheritance or fertility.
Lashana, the title Elvenbane, plays this relatively straight. She was sired by one of the magically powerful elvenlords upon a human concubine whose Slave Collar was revealed to be containing tremendous Psychic Powers. Due to the synergistic effects elven and human magics have when wielded by the same individual, Shana's raw ability is... formidable.
In Twilight, Edward can read minds and Bella can create sort of psychic shields. Renesme got the exact opposite powers. She can project her thoughts into other people's minds and ignore psychic shields.
In John Twelve Hawks' (a pseudonym) book The Traveler, the eponymous characters pass down their abilities genetically.
All of Harry Keogh's sons in the Necroscope series gain his talents in speaking with the dead, and have the capacity to learn how to use math-based teleport skills. It's implied Harry himself inherited at least his "Deadspeak" from his own mother. The Distant Finale of the series implies that all Espers eventually pass their abilities on to their descendants.
In the Chronicles of the Kencyrath series by P. C. Hodgell, the Highborn of the Kencyr can at times be so psionic that their powers blur the boundaries of reality. It's strongly hinted that their abilities are due to genes implanted from the even more powerful Arren-Ken, which occasionally manifest as felinoid body parts such as claws.
Important matter throughout the Kroniki Drugiego Kręgu series. No one knows why only boys are born with magic, or why some mages are insanely powerful, but others seem to have no talent at all. The ruling magical class (whose ancestors are said to have conquered their land with a sword and magic) is desperate to find out, because they are slowly dying out and their Super Breeding Program doesn’t give any results. There are hints it may be connected with a recessive, sex linkage gene (that’s why magic seems to be passed on from the mother’s side and why there are so few female mages). Later the heroes discover that citizens of a neighbor country (descendants of the original inhabitants) also have a magic potential, which goes against already established beliefs. In the end it turns out that the native inhabitants of the continent always carried magical genes and the invaders’ blood was only a catalyst that let this potential truly manifest. That’a why most people of Mixed Ancestry are so powerful.
In the Mistborn setting, genetics plays a direct part in whether or not someone is born with Allomantic or Feruchemical powers. As a result, the Lord Ruler set up a deliberate program and laws to control the superhuman genetics, with only nobles being allowed to have Allomancy, and killing any of the "skaa" commoners who possess these powers (and going so far as to mandate the execution of any skaa woman whom a nobleman sleeps with) as well as genociding anyone with Feruchemy.
In The Wheel of Time series, channeling comes in two stripes: some have the ability, and can learn to use it, and a very few have the spark, and will use it at a certain age whether they mean to or not. The implication is that the spark is a recessive trait, and this is supported by its being more common in isolated populations, and the fact that it is becoming rarer in men, who have been culled of the ability for millennia.
In the Star Trek Novel Verse, as of The Fall, Benjamin Sisko is watching his daughter Rebecca very closely, ever alert for any possible sign that she's inherited powers or abilities from the wormhole aliens, due to Sisko himself being "part Prophet". The idea that she might have is disturbing to Sisko, to say the least.
Live Action TV
Heroes goes with the second of the four options; the children of heroes are almost certain to have powers of their own, but the child's powers are rarely related in any way to the parents'.
While Matt seems to have the same powers as his father; Nikki, with super strength, and DL, with phasing powers, somehow manage to have a kid who can talk to machines. The latter example is ridiculous, as the entire premise of Heroes revolves around human evolution. Someone should tell them that this isn't how natural selection works. (As if they'd care.)
The whole reason Micah (the aforementioned technopath) even exists is that Linderman arranged for Niki and DL to meet, marry, and have children, so that he could then use Micah to (in a roundabout way) seat Nathan in the Oval Office.
Nathan is the exception to this rule. He's the only one in the family who wasn't born with powers and instead got them from a Super Serum. He manages to keep both this and the fact he has a power at all a secret from many characters, eventually leading to him having some sort of Hitler-esque Fantastic Racism against people with abilities. He gets over it.
Disney Channel's original movie, Up, Up, and Away features the fifth example, in which a teenage boy and his superhero family come to terms with the fact that he will never develop superpowers. Just for the record, yes, the movie does actually end with them doing just that and him not gaining superpowers. Quite possibly the sole example, at least in regards to main characters who the audience is supposed to care about.
Medium has variant 1, as all three of Allison Dubois' daughters inherited psychic powers. Her half brother also has them, which raises as yet unanswered questions about whether any of their parents were psychic too.
Although Spock is half-Vulcan/half-human, it seems that Vulcan traits are extremely dominant, as it is constantly emphasized how his Vulcan physiology differs from humans. He possesses Vulcan anatomy, as well as their telepathic powers. In fact, the only time the physical aspect of his human ancestry comes up is in regards to his viability as a blood donor for his father.
Deanna Troi is half-Betazoid/half-human. Betazoids are physically closer to humans than Vulcans are, but possess extensive empathic and telepathic abilities. Deanna seems to have inherited a watered-down version of these, being mainly empathic, but able to communicate telepathically with other telepaths. It comes up on the show that most Betazoid descendants with three-quarters human ancestry do not generally exhibit any psionic ability.
In one very peculiar instance of non-genetic superpower inheritance depicted in the episode True Q, a young, seemingly human, woman born to two parents who were secretly members of the Q Continuum is herself a Q, complete with functional omnipotence that she is unaware of. To all available tests she seems to be human. But Q causes her to invoke her powers by triggering a warp core breach while she is in Engineering, leading her to instinctively use her powers to stop it. She subsequently uses her Q powers very easily.
In Stargate SG-1, some humans inherit Ancient genes, though the only "super power" they provide is the ability to be recognized as a valid user by Ancient technology.
Not really. In Stargate Atlantis it is said that many tech that requires the ATA gene can be controlled mentally by those who have the gene. Sheppard himself says about the puddlejumper that "a lot of fighter pilots would kill to fly this thing; it's like it reads your mind..." Cue the jumper displaying a sensor readout on the windshield and dispensing a life sign detector when he wonders about how they should find their target.
Also the ATA gene is completely artificial; it was created by the Ancients for the express purpose of having a genetic marker they knew would be unique to their species.
They are not "children" of the primarchs in a true sense. They are born normal but then become Space Marines only through a regime of gene-therapy, hypnotic suggestion, artificial biological implants (extra heart, venom glands etc.) and mental, physical and spiritual conditioning. It is not genetics alone that grants them super powers. Because of the hypnotic and mental conditioning, it is also possible that they do not have "genetic memory" but have certain memories implanted (such as Sanguinius' death for the Blood Angels).
The gene-seed, containing "mental, physical, spiritual, martial, and fraternal characteristics" and being collected from any casualty and passed down, counts either way.
Exalted's Dragon-Blooded work this way. For any given child of a dragon-blood, case 4 or 5 will be in effect. There's about a 60% chance of a child of two dragon-blooded parents Exalting, and that decreases if one of the parents is mortal.
Similarly, the children of the celestial exalted also inherit diminished forms of the powers of their parents and can (in rare cases) pass those on to their own children.
The whole point of the Slivers from Magic: The Gathering, with an additional step. They eat things, then assimilate the genes, then have kids, and their kids have the prey animal's advantages. Oh, and those advantages can be shared with any other Sliver in the area.
In both Werewolf: The Apocalypse and Werewolf: The Forsaken games, being a werewolf is a hereditary thing, but that doesn't necessarily mean all children of werewolves will Change. The coupling between a Changed werewolf and the unchanged child of a werewolf (known as either Kinfolk or Wolf-Blooded, depending on the game line) has a greater chance of producing a werewolf; relations between two werewolves typically leads to bad things. First-generation children of werewolves typically have the greater chance of undergoing the First Change, but those further down the family tree may suddenly undergo the Change themselves.
Pokémon has types 1 and 3. Baby Pokemon can inherit any move both their parents know, that they could get by Level Grinding. They can also inherit TM or HM moves, or certain moves that can only come from breeding, from their fathers. Thus, it's possible to have a level 1 baby slinging Frickin' Laser Beams around.
Further, you can increase the chances that an offspring inherits its mother's Nature by giving her an Everstone.
They can also inherit up to 3 IVs (Individual Values, the genes' equivalent in Pokémon) from their parents, the other IVs being set by Random Number Generator. In 4th Gen, equipping a parent with a Power item allow the child to inherit the IV linked to the Power item (example: equipping a Power Bracer on a parent will make the child inherit the Attack IV of this parent).
Touhou's Reimu Hakurei benefits from this so much it's not even funny. As a Hakurei, she gets superpowers related to boundaries and barriers that was given to her bloodline to maintain the Great Hakurei Barrier. It's thanks to this that Hard Work Hardly Works, while The Rival Marisa has to go a relative Charles Atlas Superpower route to catch up.
There's also her rivalmiko, (well, other rival, at least,) Sanae Kochiya, who is actually blood-related to the Goddess that she serves, and as such has innate divine magic.
Though not superheroes, Apollo and Trucy benefit from this. They both inherited this ability from their grandfather and mother. Interestingly, Apollo seems to be the only one who uses the power for anything more than poker.
The ability to channel spirits runs in the Fey bloodline...sometimes. Despite being born first Morgan Fey had no powers and was reduced to being part of the branch family, in service to the main family of her younger sister Misty. This understandably caused her a bit of stress. It must be recessive or something, as her daughter Pearl does have channeling powers.
The Dragon Age games imply that magical ability is transmitted genetically; Leandra Amell of Dragon Age II remarks that magic has always run in her family, and considering that her husband was a mage it's unsurprising she has at least one mage child. She's related to the family of the mage PC from the first game, who had several mage siblings...all of whom were taken from their family by the Templars, one after the other.
FEAR zig-zags this trope. While genetics are apparently at least some factor in psychic ability, the fetus must also gestate in the womb of a powerful psychic mother to reach its full potential. This is how the Point Man and Fettel were so powerful.
In the Mother series, many of the humans with PSI attained their powers from alien genetics in their ancestry.
Part of what makes Samus Aran such a high achiever is the Chozo blood she was infused with as a young child.
And, thanks to Metroid: Fusion, she also has the DNA of a metroid. You know, those monsters that are pretty much invincible to all but ice. And classified as WMDs.
The Paralouge children from Fire Emblem Awakening inherit their parents skills via Lamarck Was Right. Players often have certain characters paired up or have them change classes before the paralouge stage so their kids have inherit devastating abilities and very high stats they normally wouldn't get in their starting class or gender ((such as giving male characters Galeforce)). Speaking of which, most the kids (with a few exceptions) are also the same starting / Base class as their mothers...
This is lampshaded, like everything else, in Girlchan in Paradise!!. Ken-Star is referred to repeatedly as having "thaaaaaaaaaat bloodline", but we never see what it does.
Girl Genius uses genetics to pass down the "Spark" — a superhuman talent for and obsession with a particular branch of science or technology. Although as yet there's not that much data to go on, the Spark appears to have greater strength in successive generations, especially when combined across multiple ancestral lines. The greater your spark, the crazier you are. Maybe the inbreeding helps a little with the craziness, too.
In Evil Inc.., Captain Heroic and Miss Match's son, Oscar, appears to be an example of Option 5 (Though he's only five, that so that could change). He uses a suit of Powered Armor provided by his grandfather, Commander Heroic, to keep up with his peer group.
The original Mr. Mighty was the grandfather of the current Mr. Mighty. His wife is a normal human; one child is a mix of Options 1 and 2 (her Dad's powers, plus shoots force beams from her eyes), the other is Option 5 (no powers).
Also, Dot Dash's son appears to be Option 5 as well.
In Juathuur, affinity to shift, shadow and shard magic is inheritable. People of other bloodlines can learn a few tricks, and that's it.
The three sons of Luk River from Irregular Elis have powers like his father.
Averted with the Kids and Trolls in Homestuck. Despite having god like powers, there's no indication their parents ever had anything abnormal about them, beyond being really badass. They aren't genetically related to humanity (or trollanity) anyways, so it's possible that either their parents carried recessive genes for their powers or Sburb itself empowered them in some way.
Seems to be a recurring theme in some of Tiffany Ross's GNIPs
In The Cyantian Chronicles "Elites" had ancestors who were genetically modified by a conquering alien race as pit fighters, as such they have a Healing Factor, Super Strength, extended life-spans, and other powers depending on their species. The traits sometimes skip a generation though, it appears to be recessive.
More recently are some of Exotica Genoworks' militia products, most notably the Siracs.
Lexx of Alien Dice is supposedly part of a bloodline of "enhanced" Rishan, as such the Alien Dice Corporation is desperate to keep ahold of him and any relatives they can find. On one occasion they offer him freedom in exchange for sperm samples.
The currently on hiatus comic PURE portrays a socially Darwinistic city-state where people without superpowers of some kind are euthanized at the age of 18 to keep them from contaminating the gene pool. Members of the de facto royal family tend to share powerful telekinetic, telepathic, and teleportation abilities.
In A Mad Tea-Party, Connie and Matilda, the two main characters, have inherited some but not all of their parents' genetically enhanced abilities.
In El Goonish Shive, aptitude for magic is inheritable and if one's lineage contained lots of powerful magic users one would be more likely to be able to gain access to powerful magic. Sometimes though this goes the opposite way and one becomes a Muggle Born of Mages. The character Ted turns out to be something of an anomaly, not only does he not inherit any magical ability from his mother's lineage, he lacks even the baseline-human natural resistance to magic and spell craft. This turns out to have both pros and cons, but has also driven him to use his great intellect to develop Magi Tech for himself and other non-wizards to be able to enjoy all the fun and useful aspects of magic.
The Global Guardians PBEM Universe is an "unlimited source" setting, where superpowers can be gained through any possible way that can be imagined. Nevertheless, and regardless of what real-world genetic science says, its guaranteed that the child of two superhumans will have either the same powers as one of their parents, or a mix between the two. (Children with only one superhuman parent tend to have a 50/50 chance of getting either the same powers as their parents, or else no powers at all.) People who get their powers from technology don't count.
In the Whateley Universe, all of the above (well, really all but #3). Mutants are people who have manifested (usually around age 14) powers based on a 'meta-gene complex' in their DNA. For unknown reasons (since no one understands why some people with this complex become mutants and others do not), children of mutants are much more likely to also become mutants. At the Whateley Academy (a high school for mutant kids set in scenic Dunwich New Hampshire), there are currently kids who have powers utterly unrelated to their parents' powers. But there is one girl who looks just like her mother used to, and has an exact copy of her mother's powers, right down to the ability to manifest something that looks like a big ol' flaming sword. There are also two students who are the kids of one of the world's most notorious supervillains, and they have his trademark forelock horns (along with his unattractive facial features), but different powers.
Averted, zig zagged, and reconstructed in Worm. Powers purchased from Cauldron are successful regardless of genes, though there are variables that affect physical mutations, the nature of the powers, and the strength of the powers. Zig zagged because most people gain their powers from traumatic trigger events, but the children and siblings of parahumans have easier trigger events to the extent that third generation parahumans are capable of triggering at age 5. However, even adopted children can gain powers more easily because even close proximity to parahumans can make it easier also. Reconstructed by the superpowered gang The Fallen, who commit incest in the hopes of having more kids with superpowers.
In Avatar: The Last Airbender , every descendant of the Fire Nation royal family is an extremely powerful bender or will be one. Bending is stated to generally run in family lines, but there are also plenty of examples of benders whose parents never had the ability and children born of benders who don't inherit it.
In The Legendof Korra, Aang(Avatar/ Air Nomad) and Katara(Waterbender) have 3 kids: Kya(Waterbender), Bumi(Non-Bender), and Tenzin(Airbender). Tenzin and his wife, Pema(Non-bender), have 4 children. All of them but the youngest are Airbenders, with the youngest being inconclusive.
To add to the confusion, there was also an episode with a pair of identical set of twins where one was an earth-bender and the other was just a Muggle.
In American Dragon Jake Long, the gene that gives you dragon powers is apparently recessive as it skips a generation. This means Jake, his sister, and his grandpa all have dragon powers while his mother doesn't.
The most probable explanation is that males imprint the gene (turn it off before passing it along in a gamete). Jake and Haley were both lucky enough (25% chance of both inheriting it) to inherit the gene and since it came from their mother the gene was turned back on before being passed along.
Kim Possible plays this to a lesser extreme: the eponymous character's father was a rocket scientist, her mother was a brain surgeon, her grandmother was a kung-fuing underwater-demolitioning aviatrix, her brothers are practically miniature mad scientists, so Kim Possible would be a world-saving She-Fu cheerleader.
Kim: I guess my genetics rock.
In the My Little Pony: Friendship Is Magic, Word of God that ponies of different types (earth ponies, unicorns, and pegasi) can interbreed. The season 2 episode "Baby Cakes" confirmed when earth ponies Mr. and Mrs. Cake have twins who are a pegasus and a unicorn, which Mr. Cake explains by saying that he has unicorn ancestry, and Mrs. Cake has pegasus ancestry. "That makes sense, right?"