When you get down to it, there's not much difference between what men and women can do. Even if on average one gender or sex is more suited to the role, as long as it doesn't involve reproduction, there will be exceptions to the rule. And sometimes even then. Even with physical appearance, if nudity isn't required, there are some people who can convincingly pass themselves off as the other gender.
Not so in fiction where your access to the supernatural powers or ability to use the Applied Phlebotinum may depend on your gender. If so there are rarely any exceptions to this rule.
This trope doesn't apply to cultural gender divides, only to times when certain magic or supernatural powers are restricted to one gender. In the case of magic, sometimes the sexes will both have access to it, but use it in a fundamentally different way - in this case expect a case of Unequal Rites as they disagree over which system is better.
May be handwaved by Bizarre Alien Biology. Compare Gender Restricted Gear, mostly found in Video Games.
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Anime and Manga
Mai-Otome. Oh, gosh, how ridiculous the Techno Babble justification is...the only real justification is that they were based on the poorly understood HiME's from Mai-Hime (who had the same restriction, justified by the fact that its magic).
In Sailor Moon only female holders of Sailor Crystals/"True Star Seeds" can be Sailor Senshi. Men born with them do get powers a la Tuxedo Mask but aren't really Sailor Senshi. Also, this is why there is no Sailor Earth as Mamoru has that Sailor Crystal. Male holders of Sailor Crystals are very rare.
This is a major plot-point in Mnemosyne. When a time spore enters a woman's body, she becomes immortal. When a time spore enters a man's body, he becomes a mindless winged killer (called "angels") whose survival prospects are rather grim.
The anime also is one of the few series to explore the Third Option: intersex (ie, people who are both male and female at the same time). If a time spore enters one of them, they get the best of both sides, becoming immortal with the ability to fly and enhanced strength.
G Gundam makes a minor point of this near the end, where Ulube is reading over the research notes about the Devil Gundam, explaining why Wong wanted Allenby to be its core. It's justified that since the Devil Gundam was meant to be the ultimate lifeform, it requires an organism capable of creating life, a woman, as its core. According to the show, the ability to give birth makes women the "top of all living things" and have the most amount of energy.
Intentionally subverted in Shitsurakuen. Only men are allowed to wield the Weapons, while women are forced to be their submissive Contracts that supplies the Weapons. The protagonist is seemingly a Big Bad-approved Spanner in the Works, a girl with the determination to rescue the girls from their fate, given the tools necessary from the academy that instituted the male-dominating rules.
Justified Which is because the race that made them put them in gender lock for females only. . . except for the fact that the male pilot also is a male mech. It also restricted certain functions in the mechs as well.
Partial subversion in Claymore. Claymores are all women not because men can't be given the same yoma-infusion, but because it's a bad idea; women are statistically less likely to go insane and become Awakened Beings than the men given the same treatment (which is not to say it doesn't happen).
The explanation given was that women have better self-control over their temper than men, so they're less likely to be goaded into accidentally going over their limits. Also, the process of going over one's limits and awakening, while excruciating, is also orgasmic. Men have less restraint in their sexuality, so they're less likely to pull back from awakening, unlike women, since All Women Are Prudes.
The title characters of Kämpfer have to be female. When a Kampfer bracelet finds its way onto the wrist of a boy, it turns him into a girl whenever he becomes a Kampfer.
The titular Infinite Stratos can only be piloted by women. The protagonist is the first male who can operate said device.
In Shikabane Hime only young women within a certain age range can be made into Shikabane Hime.
In Kinnikuman Nisei, it is declared that the "Burning Inner Strength" can only be attained by the males in the Kinnikuman family.
In Zettai Bouei Leviathan, it's explicitly stated in the intro to episode 4 that only women are capable of using magic. Though for some reason Bahamut's father is called a mage and has powers.
In The Sandman certain forms of magic (such as walking the moon's road) are exclusive to women; even a male to female transsexual can't go. There was a passing reference to the Sandman example being based on chromosomes (the character who brought it up didn't know a whole lot about the subject) while Word of God suggest that the ancient deities and witches just can't get over some old prejudices; there is nothing that inherently prevents a biological male from practicing "female" magic, except a deity that can't get her head around the idea. As seen later on, Death feels no need for such discrimination.
The Darkness only gets passed to males. When a son is born, the current Darkness user dies, and the kid inherits the abilities when he goes through puberty. Luckily for Jackie, he had a daughter.
For the most part only women can wear the Witchblade, though there has been at least one male case.
Jean Auel's Clan Of The Cave Bear is a dual literary example. The neanderthals featured in this novel live their lives along sharply divided gender lines, and due to how their brains are structured, cannot do otherwise. It's not tradition that says male neanderthals hunt and females take care of the kids. Rather, they are literally hardwired into these roles and cannot function when taken out of them. Ayla, being a modern human, can and does, deeply disturbing them in the process. Yet, her jaw almost drops when she sees Jondalar, a man, cooking.
Ironically, it's now believed that Neanderthals had less of a gender divide than Cro Magnons.
An enforced case in Terry Goodkind's Sword of Truth series. There are only female Confessors, but not because males can't get the power. It's because when a male has the power, it's a much stronger version, without the cooldown that female confessors have, and because of this they end up using said power to get everything they want. After the first generation of tyrannical male Confessors was dealt with, all male Confessor babies are killed shortly after birth.
There's also differences between Wizard (male) magic power and Sorceress (female) magic power. In practical terms, they can do more or less the same things: Throw wind, fire and lightning around, create spell forms, etc. But they're stated to work differently, such that each gender doesn't properly "get" how the other works. At the Palace of the Prophets, for example, it takes several hundred years for the sorceresses to teach young wizards how to use their gifts properly, but it takes a much shorter amount of time for a male wizard to teach another male wizard.
In Frank Herbert's Dune universe, only women could be Bene Gesserit. They had a long standing breeding program to try and create a male Bene Gesserit who could access the full range of their special abilities, which relies heavily on access to the "ghosts" of their ancestors for their memories, advice and training. And the ability to hear said ghosts is based on chromosomal memory, so women can't reach their male ancestors. Their attempts to create a male who can access the full abilities and all his ancestor's memories involved the initiation rite for becoming a Reverend Mother, which involves a toxic form of Spice and resulted in either the ability to access your ancestral memories or dead. Before Paul, all males who tried died. Mentats can be both genders, but there were no female Mentats in the book and there may have been an implication that significantly more males become Mentats.them.
The Wheel of Time has a great variety of differences between male and female channelers of the One Power. For instance, women draw from the saidar half of the Power, are able to gauge each other's Power Levels by proximity, can initiate links with other channelers to combine powers, and typically have better mastery over Wind and Water. Men draw from the saidin half, can use Fire to take in and redistribute heat (women can only take it in and consequently burn themselves or even burst into flame), can naturally sense women channeling by way of goosebumps, are much stronger on average, and typically have better mastery over Fire and Earth. How various weaves are formed is also gender-dependent: women create Gateways by making two areas 'similar', whereas men bore holes into the fabric of space.
As well, men and women approach control of their respective magics differently: women control Saidar subtly, gently encouraging it to do as they want, and lose control as soon as they try to force it to do something. Men, on the other hand, must seize Saidin, controlling it by force and fighting against it, or they will be killed by it.
Men and women can't even see the flows that the opposite sex channels most of the time, and can only block them by use of a special weave.
Quite a lot of these distinctions is drawn from the philosophy of Yin ("soft" control, passiveness, air, water, etc.) and Yang ("hard" control, aggressiveness, fire, earth, etc.).
Interestingly, we've seen The Dark One resurrect two of the Forsaken in opposite-sex bodies, without any change in their power type or strength. So either souls have an innate sex or this is the Dark One we're talking about and further speculation is pointless.
In Christopher Stasheff's Warlock of Gramarye series, psis on Gramarye have sex-linked powers — Witches (women) are telekinetic, and Warlocks (men) can teleport and levitate themselves. The hero and his family are the only exceptions, due to not being entirely out of the same gene pool.
Averted on the Discworld, at least in the areas where most stories featuring wizards and witches take place. Wizardry and witchcraft are separate forms of magic which are mostly gender divided, but this is a social not biological split related to prejudices on both sides of the fence. Exceptions do exist, such as the early mention of wizards in Krull not caring much either way. Terry Pratchett's opinion, at least referenced in a narrative aside, is wizardry being systematic was more suited to men while witchcraft being initiative/emotional was more suited to women. Interestingly, despite her initial reservations, Granny Weatherwax is eventually convinced that Eskarina's mindset is wizard-like and that trying to shape it into witchcraft simply because she's female is a bad idea.
Sourcery, however, remains a purely male avocation, what with the eighth-of-eighth-of-eighth son rule.
Partly subverted in Kelley Armstrong's Otherworld. Witches are female, sorcerers are male. They can use each other's magic, but not as well as the proper users can. Witch magic generally relies on incantations or healing brews, while sorcerer magic uses gestures. Witch and sorcerer genes are sex-linked and supposedly incompatible with each other, requiring them to breed with mundanes. However, there are hints in Dime Store Magic and Industrial Magic that witches and sorcerers may be more alike than they think, particularly the revelation that neophyte witch Savannah Levine is the daughter of a witch and a sorcerer, supposedly impossible. It is also pointed out that social stigma prevents sorcerers and witches from having sex together.
Industrial Magic suggested that sorcerer magic and witch magic are branches of the same school. Witches only know the first level of their magic, as they eschew the second level spells (such as curing hiccups) as useless. Unfortunately for the witches, learning the second level spells is the only way to unlock the upper tier spells (contained in the witches' own Great Big Book of Everything, but dismissed as unworkable). Most supernaturals dismiss witch magic as weak and useless, as both witches and sorcerers believe that the basic tier of witch spells is all there is.
Andre Norton's Witch World has female virgin witches. They are shocked when Simon Tregarth, a man from another world, has the same powers. (And more shocked when a witch marries him and keeps her powers.)
It's implied that the differences in magic are due to training rather than innate ability, as female elves in that society generally have little freedom, and are only taught "small" magic. There are brief mentions of powerful elven ladies who learn to wield magic in a masculine way. Also, some male elves have difficulty with using small practical magics commonly used by females simply because they haven't been trained in the same way.
The Earthsea Trilogy featured mostly male wizards. In fact, there was a proverb "As weak as a woman's magic." This is — altered in later books.
In His Dark Materials, in Lyra's world witches are a One-Gender Race, possessing magical tendencies and long life. Their male offspring (fathered by human males) are normal humans. Male witches did exist elsewhere in the multiverse, though they are only mentioned once.
In First Lensman, Mentor explains to Jill why it is impossible to create a Lens for a female. Mentor is lying his head off, as Clarissa will prove later in the series, but for the first couple books that's how the Lens works.
He's not exactly lying, given that he also outright tells her that there will at some point be a female Lensman. He doesn't, however, mention her daughters, who I guess aren't technically Lensmen ... they just have all the powers even without having a lens and can generate their own out of thin air purely by thinking hard.
In the Sector General novels, Educator Tapes can't be tolerated by human females. This started as Values Dissonance because the first book was written in The Fifties, but we later learn that it's a species restriction; alien females (those species that have females) can and do use them.
In Garth Nix's Old Kingdom trilogy, the Clayr (prophets who live in the glacier) are almost all women; the rare occurence of male Clayr are seen as anomalies. Plus Clayr who choose to have children with men generally always have daughters.
In Anne Bishops "Black Jewels" saga, female magic is almost always more potent than men's. Ranking within the Jewels can extend to Queen for females, whereas male ranking extends only to Warlord Prince. However, the magical power depends on the darkness of the jewel of an individual.
Holy spellcasters in The Banned and the Banished get their powers either from the god Chi (for males) or the goddess Cho (for females.) The two deities are equally powerful, but Chi splits his power among a large number of casters, while Cho only gives her power to one woman at a time. This means that female casters can store twice as much Mana and have access to three times as many spells.
Almost the case with the Jordain in Counselors and Kings. Jordaini girls are almost always stillborn, so that the vast majority of actual Jordaini are men, but occasionally a Jordaini female will survive. Cassia, Jordain to King Zalathorm is the only one we actually meet. It turns out that Tzigone, one of the main protagonists, is a Jordaini birth gone wrong, so she has the Anti-Magic abilities even though she's not considered a Jordain.
In the Thieves' World series, only men can become mages. There are, however, indications that this is a social restriction with no inherent basis.
In Three Days to Never by Tim Powers, one of the characters is a sorcerer who, it turns out, was born female and went to extreme lengths to gain access to male magic.
In Sergey Lukyanenko's Dances in the Snow, FTL Travel is fatal to women (at least, human women). The reasoning for this is never explained. However, the only way for women to go to other planets is by becoming a Human Popsicle. This also leads to a lot of sexism, particularly from starship crews, who derogatorily refer to women as "cargo". At the end of the novel, it's mentioned that a genetic cure has been found to allow future women (not the ones being subjected to gene therapy but their children) to survive FTL travel and even become pilots. None of this is mentioned in the original novel Genome (Dances in the Snow is its prequel), where Genetic Engineering is the New Nuke, so this is no longer an issue (two of the main characters are women and have no problems surviving space travel).
Only the women of the Lyud' can use normal magic. A Lyud' male using magic means that the situation has already somehow passed the Lyud's Godzilla Threshold.
Only the men of the Chud' can use magic.
The Moryana creation rite can only be survived by a woman.
A Daykini can only take a female host, although not restricted by species.
All Tat' Lords are male.
In If I Pay Thee Not In Gold by Mercedes Lackey and Piers Anthony, only the women in Mazonia have magic (of conjuration). As a result, all men are either slaves or treated as second-class citizens if they've been set free.
In Sheri S. Tepper's world of the True Game, several of the Talents are gender-limited, or at least rare in one or another sex. Healers and Midwives, for example, appear to be mostly female, while Armigers, Sentinels, and possessors of Necromantic Talents appear to be mostly male. Harpies and Queens are of course always female, while Kings and Princes are of course always male. (Though given that many women amongst the Gamesmen are encouraged to hide or deemphasize their talents, it's hard to know how common certain talents really are amongst them.) Of course, it's all rendered moot when, at the end of the Jinian series, The Magic Goes Away except for Midwives.
In Kroniki Drugiego Kręgu only boys are believed to be born with magic. It’s later subverted with introduction of Jagoda (a very powerful female Observer) and as the series goes on more and more girls with magical abilities are discovered. They still remain much rarer than male mages through, which makes them (especially Jagoda) very good candidates for the Super Breeding Program.
In Andre Norton's Storm over Warlock, the Wyverns who can dream are all female. They are surprised to find males who can dream even among humans, and despite their margial acceptance of that, Thorvald appoints Charis in Ordeal In Otherwhere to be the person actually dealing with them, as a female.
Among human wizards in the Young Wizards series males have an affinity for the elements of fire and earth, while females have an affinity for water and air. This generally doesn't matter much, except in Wizards Abroad, when the characters have to deal with Empathic Weapons which are embodiments of the four elements.
Live Action TV
In Battlestar Galactica, while gender is apparently irrelevant for most professions, including the priesthood, oracles, who have prophetic abilities and can tell the will of the gods, have been women in every case we have seen or heard of.
In Buffy the Vampire Slayer, Slayers are always young girls. Averted with witchcraft - though most practitioners are female, there are male users - Giles borrowed the power of an entire coven to take on Dark Willow, Angel and Xander are both shown to use spells, Oz and his bandmates accidentally summon the demon of fear, and there are a few guys in UC Sunnydale's Wicca group. On the other hand there are no real prominent good male dedicated spellcasters on the show to contrast with Willow, Tara and even Jenny Calendar. There are powerful but not "good" male spellcasters such as Rack, Ethan, and Jonathan.
It should be mentioned one of the ways for people whom today we would consider homosexual or trans-female could live openly and still be moderately tolerated in Norse society was to practice witchcraft (much like the Hijira of modern India). Of course, they were still shunned and ostracized, but people still sought their services, and not many would want to anger a witch.
And to further make the point: Odin is a male witch. (He wanted to learn all the magic of the world...) This means exactly what you think it means.
Justified, since the enhancements are based on the biology of the Primarchs, who were all men because they were cloned from the Emperor.
Older source material also stated that acceptance of the implants and the ensuing muscle growth required the increased testosterone output in men.
In Warhammer both the Dark Elves and Bretonnians only have female magic users. Whether this is a cultural or natural restriction depends on who you ask; males of other factions are perfectly able to use magic, but each faction accesses and uses magic in a different way.
In at least some versions of the fluff, the lack of male Dark Elf wizards was related to a prophecy that one of them would topple the immortal Dark Elf king. Obviously, male study of magic was not encouraged.
Vampire: The Requiem features the Qedeshah bloodline, a motherly lineage who draw their origins from a group of temple prostitutes. Part of their bloodline-specific curse is that after joining the bloodline, they can only Embrace females. Attempts to Embrace men result in the man experiencing agonising, incapacitating pain for 24 hours before they expire horribly, the Qedeshah "mother" suffering a portion of this pain through the sympathetic connections of their shared blood. Men are not barred from joining the bloodline from outside the family tree, but upon doing so their vitae is rendered sterile and they can no longer Embrace childer or create ghouls, earning them the position of eunuch.
To be clear, female Immortals do exist, although they're outnumbered 10 to 1 by the males. (Immortals are fond of joking about how their progenitors weren't quite as sexist.)
In the 2E Ravenloft setting, the followers of Hala included female clerics and male wizards, ostensibly because the goddess taught that each gender was better-suited to that sort of magic. Subverted in the 3E Ravenloft products, which left its Halan prestige classes open to both sexes.
Also, the only Vistani to be gifted with the Sight are females. This is because a long-ago prophecy warned them that a male Seer would one day become the dreaded Dukkar and destroy their people, so they kill any male offspring that develop the Sight.
In BIONICLE, only the female Skrall have psionic powers. However, it turns out that these were given to them by an Eldritch Abomination purely for it's own amusement, and are not a natural ability at all.
In the Ace Attorney series only Fey women can be mediums. This actually causes massive social damage to the Fey clan - because the Fey family holds their spiritual powers so highly, their men feel deeply unappreciated, and their home village, Kurain, has one of the highest divorce rates in the country. (Maya implies that her young cousin, Pearl, hasn't seen a successful relationship in her life.)
The Sorceress power in Final Fantasy VIII is only passed down through women, with each woman passing the power to someone else upon her death (it appears that it's usually the closest woman, so long as she holds the proper potential). This power is the central focus of the game, as every Sorceress is powerful enough to change the course of the world or control the fabric of reality itself. An in-universe legend posits that the Sorceress power is really the immortal spirit of a god who'd once gone to war with humanity and lost, and escaped by hiding himself in the body of something mankind instinctually wants to protect: women.
In Final Fantasy Tactics and A2, the Standard Status Effect preventing Ribbon accessory can only be worn by female characters. In A2 that means only Viera, Gria, Adelle, andFrimelda, but Humes, Bangaa, and Nu Mou can learn a passive ability that lets them wear one anyway. In Advance all generic teammates but Viera have Ambiguous Gender so only Viera and Ritz (who is a Viera for gameplay purposes) can wear them.
Fire Emblem has female Dancers and male Bards, though they essentially do the same thing. In addition, only females can ride Pegasi, explained at one point as the weight (amusingly, generic enemy Pegasus knights count as male stats wise). Another explanation claims that it's because it's hard enough for a woman to get her Pegasus to trust, while a man is incapable of gaining a pegasus' trust.
In the earlier games in the Fire Emblem Akaneia series the enemy pegasus knights were male, but they appear to have been have Retconned out of the series as they're gone from the remake.
In Shadow Dragon, the spell Excalibur can only be used by men and the spell Aura can only be used by women(despite it being used by a male character used it in the games story). It is also noted that Falchion can only be wielded by male descendants of Anri though this is proven false when Lucina wields it in Awakening.
In the later Wizardry games, The Lord class is male only, while the Valkyrie class is female only.
In the Ogre Battle series, males and females have entirely different classes available to them, with no class in common. The starting female class is Amazon, while the starting male class is Fighter. Some classes are obvious counterparts (The female Dragon Tamer and the male Beast Master for example). Some of the Tactics Ogre games however do not follow this formula, instead being like Final Fantasy Tactics where a handful of classes were gender-specific (like Dragon Tamer, Beast Master, Witch and Dragoon), others are shared amongst both genders (like Knights, Wizard, Clerics and Fighters).
Achaea features the Siren, a female-only race who eventually get the ability to charm others with their good looks as they level up.
In BioShock, only female children under six can be implanted with ADAM slugs. This makes them invincible and able to puke up EVE serum. they also heal instantly (this is not as good as you think, one fell down the stairs and broke both legs, which then healed cokeyed. the doctors had to re-break her legs several times to put them right). However, one researcher discovered that if you manage to restrain them and tear out the slug, you kill them instantly and get a huge shot of ADAM. Enter papa Frankestein...
In Bayonetta, only women can become UmbraWitches and only men can become LumenSages. Witches' power comes from making pacts with demons and are enhanced by the light of the moon, while the Sages commit to serve Laguna and are enhanced by the sun. The forbidden union of an Umbra Witch and a Lumen Sage is what kicks off the events of the game.
In Footloose, men's magic is (semi-artificially) restricted to the Fae realm, and there vastly weaker.
In Sacred Pie the sacred objects can only be used by men, regardless of species. This is a side effect from Lucifer creating them for his own use.
The Wotch: Wotches cannot be male, and cannot even be turned male by magic. Although, that's not to say they can't have been male prior to their becoming the Wotch.
There IS a male equivilent - Melleck Xaos is the Worlock. Their powers are a bit different, so the rule still applies.
The Law of Purple has the Myranians, a race of aliens where only the females have psychic powers.
In, Homestuck, certain classes in Sburb/Sgrub are only available to certain genders. Princes, Bards, and Lords are exclusively male, while Muses are exclusively female.
The Trait Positives in lonelygirl15 are always female, for some unspecified genetic reason.
In Trollz, only the females are able to wield magic. It wasn't always the case, but the Big Bad's attempt to take the magic for himself made it so only girls could use it. Males are left to their physical and mental skills, though older Troll males are able to use magic, still.
In Avatar: The Last Airbender , female waterbenders develop healing abilities while males (as far as we know) don't. Since the northern water tribe had a Stay in the Kitchen mentality, healing was all the waterbending female tribe members were allowed to learn, while offensive waterbending was left to the males (at least until Katara turned that on its head).
Singing voices. While there is some overlap in the alto and tenor ranges, natural male sopranos (as opposed to castrati and singing falsetto) and female basses are extremely rare and usually due to a hormone imbalance.
For modern-day male sopranos (also known as sopranists), you have Radu Marian and Jorge Cano who are called natural castrati due to endocrinological issues, and Angelo Manzotti who taught himself a special technique with his vocal chords. Michael Maniaci is the closest you'll come to a natural male soprano — his vocal chords never went through puberty, but the rest of him did.