Superheroes sometimes have an unintuitive combination of powers. Sometimes this is a Justified Trope. For example, anyone with All Your Powers Combined will have Combo Platter Powers at least some of the time. Other times it is the result of either an excess or lack of thematic unity. Sometimes, combinations that look strange to modern-day Western conceptual categories made perfect sense in the culture where they originated.
This can happen through accretion, as with Superman; as a deliberate change to the character, like the Invisible Woman; or even at creation, like the Martian Manhunter. Sometimes there will be a Hand Wave as an off-hand explanation ("Secondary mutation", anyone?) or a later Retcon to explain how the powers actually work together; other times, it just happens. The most common set is the Flying Brick.
This does not include abilities gained by learning them or some other method of choosing them, as something that can be learned is only random if the character wants to study random things. This means most magical abilities are excluded unless it happens to "natural" magic that a character is born with.
Frequently a result of when a character keeps playing the Super Power Lottery. Compare Required Secondary Powers when the oddball minor powers are actually necessary to make the main power work properly. When the character in question is some kind of god, he/she is usually one of the Odd Job Gods. When one of these powers is significantly less powerful than the rest, it's Flight, Strength, Heart. When it's the standard Flight, Super Strength, and Super Toughness package, that's Flying Brick. If it's flight + some ranged attack, that's Flying Firepower.
Sharingan (the regular ones are based on sight/perception/analysis, but the Deadly Upgrade's powers are all kinds of crazy, including hypnosis, setting things ablaze with immortal flames, summoning giant guardian deities capable of divine abilities like sealing souls or cutting an entire mountain and bending reality at will. Also, with Senju DNA, an Uchiha gains the Rinnegan's powers as well).
Rinnegan (become an Instant Expert, use all five Elemental Powers when no one else can, see chakra, summon an Eldritch Abomination that lets you animate six human bodies with their own unique power, and summon the being that has control over life and death), and the ones with them can still learn other regular techniques.
Kamen no Maid Guy: Kogarashi has New Powers as the Plot Demands, most of them completely unrelated. In addition to the standard super-strength, inhuman toughness, super-speed and the ability to defy gravity with jumping, he has a paralyzing voice, x-ray vision, levitation, Prehensile Hair, the ability to hypnotize people even without direct eye contact, hands that can evaporate all liquid from anything he rubs on, 37 senses (don't ask), knowledge of every gourmet recipe ever made, the ability to summon and direct underwear-stealing crows, and USB connectivity in his brain. For starters.
JoJo's Bizarre Adventure Killer Queen can turn anything he touches into a bomb, then detonate it remotely. And he can detach his left hand as a heat-seeking autonomous bomb. And he has a compartment in his chest which contains a flower that shoots invisible air bullets. Andhe can turn back time to initiate a "Groundhog Day" Loop whenever a certain person is asked about his secrets, which has the side effect of killing the questioner.
Rave Master: Haru Glory's Ten Commandments sword at any given time gives its wielder powers to generate explosions, move and attack at super speed, cut intangible objects and seal magic, shoot ice and fire, paralyze and push back opponents, become a ridiculously heavy sword, emit blinding flashes of light, unleash a berserk mode that features enhanced strength and speed, and finally the ability to dispel evil.
One Piece: most characters' abilities stick to a certain theme.
Brook: The Revive-Revive Fruit originally appeared to give him the ability to come back to life, once. Post-Timeskip, his powers now seem to have granted him control over his soul, which allows Astral Projection and the ability to create ice by drawing on the coldness of the afterlife. Also, Brook is a skilled swordsman.
Blackbeard: Dark-Dark Fruit powers grant at least two entirely different sets of powers: One set of powers allows him to manipulate gravity and be a living black hole (hence the name of the fruit), and the other lets him take someone else's Devil Fruit powers. So far, however, it hasn't been entirely clear how much of this he began with, how much he's taken from others, and how much are his own body's natural abilities. Nevertheless, he has a definite odd combination, now that he can not only control gravity, but also create earthquakes at will.
Perfect Strike (SEED, this is all of the packs used at once)
IWSP Striker Pack (SEED)
Destiny Gundam (SEED Destiny)
Strike Noir Gundam (SEED CE. 73 Stargazer)
Tactical Arms (Astray)
X-Men, has the concepts of Secondary Mutations, Exactly What It Says on the Tin, which are un-related to their primary mutations, and Homo Killcrop, the informal term for the original pre-modern sub-species of x-gene-possessing mutants, whose powers manifest at birth/infancy and are much more chaotic — and thus more varied —than those of the modern sub-species of mutants, whose powers manifeset at puberty (stated to be the result of natural selection, as mutant babies tended to have an extremely low survival rate compared to mutant teenagers). A number of X-characters thus fit this trope, including:
Wolverine: healing factor, retractable claws, enhanced smelling and hearing, adamantium skeleton. It's explained that Wolverine is the product of two mutant families. His mother's family has long been "cursed" with bone claws and mindless animal rages, while his father has the regeneration and enhanced senses. Wolverine gets all of them. The adamantium is added, much later in his life, by government experimentation. They'd been wanting to do it for a long while to produce Super Soldiers, but adamantium is poisonous — a test subject who could heal away the ill effects was perfect.
His son, Daken, gets all this plus pheromone powers.
Emma Frost: Telepathy and turning to diamond.
Nightcrawler: Physique and coloration give him poor-man's-Spiderman agility and shadow-camouflage. And teleportation.
Angel: Wings for flight and the Required Secondary Powers that make flight work and can heal people with same blood type. Although the last part was added later because, well, flight is boring. Angel also recently gained the ability to transform to and from Archangel, who has metal wings with razor-like feathers. That can be fired at enemies.
Icarus: Wings and associated Required Secondary Powers, the power to mimic any sound, as well as Healing Factor for himself. Unfortunately, the healing factor relied on enzymes produced by the muscles of his wings, so when they were removed, he lost that power and promptly had a Bridge Drop befall him.
Sage: a mind that works like a computer and can jump-start the mutations of those with the mutant gene but no powers (or activate the "secondary mutations" of powered mutants, which are often unrelated to their original powers, placing them in this trope's territory.) And telepathy that she rarely uses, despite being nearly on par with Emma Frost.
Wild Thing of the MC2 Twenty Minutes into the Future-verse: The healing factor and animal-like senses and hairdo of her dad, Wolverine, with a smaller dose of the temper. "Psychic claws" in the style of Psylocke's psychic blade? (It's said it was "taught" to her by Psylocke, the mental version of CharlesAtlasSuperpowers, but no one else without psychic powers has ever been shown to use one, and Psylocke's own ability to use this is at the mercy of whatever's going on with her powers at the moment.)
Monet St. Croix: Flying Brick powers. Ability to merge with any mutant member of her family encountered thus far, with different combinations having entirely different personality and powers. This goes, in fact, for all of the St. Croix siblings except for Nicole (who hasn't displayed solo powers just yet.) And telepathy and heightened intelligence.
Selene: Animate objects plus suck people's life force to feed her youth and immortality (plus some minor Psychic Powers and Functional Magic, and various inconsistently enhanced physical abilities). Until she got upgraded; as of Chasing Hellfire, it's "turn into living shadow, plus absorb people entirely to feed her youth and immortality, as well as take on the form of victims."
Cassandra Nova: Psychic Powers and the ability to give (or perhaps catalyze, a la Sage) powers in others.
Omega Red: has a healing factor and life draining powers. Super Strength from draining life, metal tentacles don't fit but were added since healing factor let him take it. Releasing clouds of deadly gas is what doesn't fit (marvel handbook calls the gas death pheromones. Sweating some sort of toxin would probably explain healing factor. Healing factor explains strength. Draining life sustains the healing factor). Carbonadium the metal that makes up his tentacles is a poor subsitute of admantium, it's radioactive which explains the source of the gas.
Gambit: power is to make stuff blow up, later HandWaved as turning the potential energy in an object into kinetic energy. His charm, though, is sometimes said to be psychic in nature. His agility is also enhanced, sometimes explained away as a subconscious manipulation of kinetic energy in his own body. Also, when he was temporary blinded, he could see glimpses of the future in his cards, a power he's never had before or since. And they were dramatically extended in the New Son/New Sun saga - in the end, his powers were basically extended to manipulation of any matter - he gained a healing factor, flight powers, the ability to make stuff explode with a mere thought etc etc etc. The powers had initially been turned off by Mr Sinister, and at the end of the saga, were 'burned out' by his exertions fighting his Alternate Universe duplicate.
Magneto: control over magnetism, which was quickly expanded to include the entire electro-magnetic spectrum. He also has telepathy, though it is undeveloped.
Apocalypse: wide array of powers due to alien/future (his Expansion Pack Past gets complicated, though not as bad as Logan's) technology, through which he can use virtually any physical superpower, as well as interface with technology. His inborn powers are merely being an insanely good fighter, a degree of Super Strength, stamina and durability, Super Intelligence, Immortality... and having gray skin for no good reason. He has also demonstrated telepathy and telekinesis, but it is unclear whether these are natural or part of the suit.
Blink: the ability to teleport herself, however she can also teleport objects away from her body by producing crystals from her body which she can throw at persons or objects and if this wouldn't be enough she also has glowing green eyes, pink skin, pink hair and natural face markings.
Marrow: mutation is to have bone weapons growing out of her body, a healing factor to survive said outgrowth and for unknown reasons pink hair and skin. She also has two hearts... to explain how she could be stabbed in one and be back later when she goes the way of all dead mutants.
Rogue: the power and Life Energy absorption, and used to have the Flying Brick package permanently absorbed from Ms. Marvel. For a time, she had Sunfire's flames-and-flight combo. Even more recently, Rogue has gained voluntary control over her absorption along with the ability to recall any and/or all of the powers she has absorbed in the past.
Legion: Son of Charles Xavier, he actually has the ability of person's psyche into his as an alternate personality, on top of Reality Warper, Telepathy and a whole host abilities but most are assigned to different alternate personalities.
Superboy: Conner Kent and Chris Kent a.k.a. Nightwing have Kryptonian powers and tactile telekinesis. Chris' girlfriend Thara Ak-Var aka Flamebird has Kryptonian powers andpyrokinesis.
Legion Of Super-heroes: Ultraboy a guy with the powers of Superman but he can only use one at a time (even the passive ones like invulnerability.) He does have a Legion flight ring so he doesn't have to use his natural flight which frees him up to use one other power. He does seem to keep the Required Secondary Powers for whichever ones he's using at the time though.
Namor the Sub-Mariner: has everything you'd expect from a being built to survive underwater: strength enough to survive ocean pressure, agility and speed to swim quickly and efficiently... and tiny wings on his ankles that allow him to fly, making him a Flying Brick. This last was eventually explained as a mutation caused by his surface-dweller/Atlantean hybrid heritage. Thus he's considered one of the first mutants of the modern age in the Marvel Universe.
Spider-Man: Most of his powers are supposed to be those of a spider, amped up to human proportions, but with Spider-Sense standing in for a spider's multiple eyes. But once having got these powers, Peter quickly invents his web-shootersnote Originally, he knew instinctively how to mix chemicals to make web, which he then loaded like cartridges into a "blaster" on his arm, which are thematically appropriate, but not really connected to the rest of his powers. Later versions of the character have given Spidey "organic web-shooters" to more closely tie his powers together. Over the decades, Spider-Man has developed other temporary powers or devices. A recent secondary mutation gave Peter more spider-based powers including the ability to feel trace vibrations in his weblines, enhancing his spider-sense to where he can practically see in the dark, making his hairs more sensitive, giving him poison stingers in his arms... and the power to instantly recognize what species a spider is by looking at it. However, most of these powers, plus his organic webbing, have been lost in the Time Skip between One More Day and Brand New Day.
Fantastic Four: Susan Storm, who started out with just invisibility, then gained force field powers to allow her a more active role in the stories. A much later Retcon claimed that her invisibility was actually an instinctive use of the forcefield to distort light around her. Johnny Storm also has the Flying Firepower set, and is over on that page.
Danger Man (nee Dan Jermain) was a hapless worker in a nuclear plant who was caught in an industrial accident that made him bigger, stronger, and more powerful. And also gave him energy blasts, the ability to breathe underwater, and he can have a meltdown if he gets angry. His head and hands glow and have little spheres orbiting around them, atom-style. Although he's also a huge subversion of the whole "radiation accident" origin; He's not a superhero. He's still a hapless worker in a nuclear plant, but now when he rolls over in bed he crushes his wife, tears his clothes up with one false move because he's so strong, and gets stared at on the subway because of how obvious his situation is.
The Hulk: He has Super Strength, is Nigh Invulnerable, can create a stunning sonic boom with his hands, regenerates, okay, all fit sort of with the "unstoppable force of rage" idea. However, two other, lesser-known powers: he can see, and HIT, ghosts and astral projections, and can home in on the site where the gamma bomb that created him went off. And supermath. The ability to automatically reduce collateral damage when levelling down entire cities. Officially, this is explained as Bruce being a 'hypermind', able to analyze and predict the consequences of his actions near-instantaneously. Hulk is also highly resistant to telepathy and mind control(it's mentioned that he was the only one who wasn't effected by the Cosmic Retcon that wiped out everyone's memory of the Sentry, and neither Professor X or Emma Frost can Mind Rape him), occasionally capable of absorbing radiation, and has limited reactive adaptation. He's shown adapting to being able to breath under water and survive for a fairly considerable time in the vacuum of space (while still needing to breath eventually). Ultimate Hulk takes it a step further, adapting to the atmospheres of Mars and Venus after limited exposure.
Spider-Woman: Mattie Franklin, one of the numerous heroines (and villains) who goes by the name. has the powers of all of them. This includes powers such as: Strength and agility, flight, energy blasts, some low-level psychic powers, psychic webs, psychic spider-legs... Logically she should also have Jessica Drew's pheromone powers, but they were never demonstrated.
Joshua Carver has super strength, flight, and quick healing.
Smoke Lightning can transform into smoke and shoot lightning.
Cerebus: Parodied with the "reads" character Rabbi. He had hundreds of peculiar and highly specialized powers such as dextrorotatory breath - making the plane of polarization of light spin to the right by blowing.
Darkseid was born with the Super Strength and Nigh-Invulnerability common to the strongest of the New Gods. Then he killed his older brother to claim the Omega Effect, which is essentially a Green Lantern Ring (the trope, not a literal one) taken Up to Eleven in the form of Eye Beams. The Omega Effect allows Darkseid to teleport people, torture them, wish them to the cornfield and wish them back. In Final Crisis he gained even more new powers. His new variant on the Omega Effect, the Omega Sanction, can subject its target to a Fate Worse Than Death by sending that person into the past to live out a brutal cycle of reincarnation. Darkseid can also create avatars of himself to do his bidding when he doesn't feel like moving himself, move through time, make himself as huge as skyscrapers, teleport without using the Omega Force, mass scale mind control, and quite a few others. This makes sense, considering Darkseid is a god.
Deconstructed in Irredeemable. The Plutonian has a wide variety of superpowers because he's actually a Reality Warper subconsciously altering the universe.
When he was being changed into a winged humanoid by Varx to save his life, there was magic left over that had to be factored in somehow. Varx channeled the magic into mild Super Strength and super-hearing because he wanted it to be as unobtrusive as possible. Why he didn't improve John's sight, which would have made more sense for a winged guy, can probably be explained by the fact that he was working very fast.
When he got his water powers, which come from a magical gem, the gods (actually Jeft) ensured that he would get the gem (rather than Paul) because it worked better on stronger hosts.
Jack-Jack can shape-shift, turn into metal or a goblin, phase through walls, fly, set himself on fire, eat wood, and shoot Frickin' Laser Beams, and that's just what we've seen so far... And he's a baby. Word of God goes that he has so many powers precisely because he is a baby. When he grows up, he will make his choice of powers.
Violet had the seemingly unrelated powers of turning invisible and generating a force field, as a Shout-Out to the Invisible Woman. As the Invisible Woman's entry above explains, those powers could be related — you might use a field of some sort to bend light away to go invisible, and if you can project a field that bends away light, why couldn't it deflect other stuff too?
Films — Live Action
X-Men: Wolverine had the above powers but with a different explanation: adamantium can only be molded in its liquid form - after cooling enough to become solid, it instantly becomes indestructible. Thus, it had to be grafted to the subject's bones in its (really hot) liquid state. Wolverine's healing factor allowed him to recover from the trauma caused by this (and thus was the reason he was chosen for the super soldier program). His claws were also implied to be implanted, rather than part of his skeleton, although this was later retconned in origin movie.
Callisto: Super Speed and the ability to detect other mutants and the nature of their powers, apparently at any distance (she was how Magneto found the caravan transporting Mystique.) A result of telescoping the powers of several Morlocks into one character for the movie.
Dracula: is supremely strong, hypnotic, commands animals, can turn into a mist, addict people to his blood, and climb walls like a spider. Most of these powers can be found in folklore about vampires, or previous vampire novels, but not usually all at once. And just what constitutes "vampire powers" is under dispute — see Our Vampires Are Different for further discussion.
Codex Alera: Even a single-element Crafter will get an impressively broad array of powers. As an example, an Earthcrafter can gain superhuman strength, shift rock and earth to create barriers or tear down walls, calm animals, travel rapidly over the ground, inducelust, and sense people's locations if they're on the ground. Tavi is smart enough to recognize the implications of this, and when he is short of combat engineers enlists the local brothel to aid a demolition project.
The Chronicles of Amber: The Amberites basic package includes superhuman strength and endurance, regeneration, telepathy and dimension hopping; various family members also have prodigous weapon skill, sorcerous powers, or shapeshifting. Most of these make perfect sense given their background (part of which you don't find out about until fairly well along in the Chronicles, because Corwin himself doesn't know it). See the series page for more details.
Allomancers have quite an impressive array of abilities, including Super Strength, Super Senses, emotional manipulation, limited telekinetic control of metals, and Combat Clairvoyance. Mistborn have all of these at once. Justified in that they get their abilities by metabolizing certain metals, each of which has distinct effects- a Mistborn without his or her metals is no more powerful than any other human.
Feruchemists from the same series have a similarly broad array of powers, because of their ability to alter their own bodies' processes through Equivalent Exchange. It's well within a Feruchemist's abilities to have Super Strength, Super Senses, a Photographic Memory, a Healing Factor, and more—as long as they're willing to go with their abilities similarly reduced for an equivalent amount of time.
Compounders are people born with a matching allomantic and feruchemical ability. Due to a quirk of the magic system, this lets them break the Equivalent Exchange, getting more out of their feruchemical powers than they put in, creating an infinite loop. One man uses this for Ageless Immortality, and another for a Healing Factor that makes Wolverine look like a wimp.
In the Circle of Magic universe, ambient mages usually have one type of magic. They might have a more limited or a more broadly defined ability- a smith mage might have magic with all metals, or just with iron, for example- but their magic will still be with one kind of thing. And then there's Kethlun Warder, from the second series- who has glass magic and lightning magic- two completely unrelated types of ambient magic. Handwaved, as the lightning magic was stated to have been a result of him being struck by lightning and mixing with his ambient glass magic, which kept him from being killed.
in Xanth non-humans and Half-Human Hybrids with Talents often fall under this trope, inherting one or both parents' species abilities plus their own unique talent. For example; Surprise Golem can inherited her mother's size changing ability (she can go from doll-sized to normal human) along with her own unique Talent of... giving herself any Talent she wants. Though she's limited to one talent at a time and once she's used a particular variant of said talent, it's gone for good.note This was found out not to actually be the case. The variants can be reused after a certain amount of time. But this revelation was wiped from her memory, so no one knows this as of now.
The Haitian can block the powers of other 'special' people. Also, he can erase memories.
And as of season 4, Matt Parkman has gained the power to paint the future, despite already having powers of his own.
Interestingly, an episode also showed him flying, but it turned out to have been Just A Dream.
Santiago's father from the webisodes, who has the same power as Santiago himself, plus electricity.
Ando eventually acquires the ability to boost the superpowers of others by touch; this ability apparently manifests as red lightning that can blast people with concussive force.
"Baby Touch-and-Go", whose touch can activate or deactivate electrical and mechanical devices, and... superpowers?
Charmed: the Halliwell sisters have at various times suggested that their powers are supposed to grow with time and use, and some future versions of them bear this out — Piper freezing whole city blocks, Prue accidentally demolishing part of the house with a careless handwave. But the actual power sets they develop over the course of the series don't match up so well — Prue adds astral projection to her telekinesis, Phoebe adds levitation (and empathy, which sort of works) to her premonitions, and Piper adds blowing things up to her freezing time. All of these were handwaved to some extent, but they certainly don't match at first glance.
Farscape has a lot of characters with a lot of weird powers, but Sikozu really takes the combo platter to new levels: she can re-attach lost limbs, walk on walls, and, near the end of the series, it's revealed that she is a walking anti-Scarran Doomsday Device. At one point, she expresses mild surprise that other people can't do it. Of course, it's revealed that most of her powers (with the exception of the wall-walking) was due to being a bioloid infiltrator.
She can also learn any language in record time, which is a good thing because she's allergic to Translator Microbes.
Kamen Rider series: Some have Riders whose power is to mix-and-match:
Kamen Rider OOO takes this further, able to select different powers for his head, body, and legs; with five options for each. At least OOO's powers are tied together by an animal theme. For example, his default form has the eyesight of a hawk, the claws of a tiger, and the leaping ability of a grasshopper. And again, this is before counting the dinosaur-themed Super Mode (which can't be mixed with any other powers), nor is it counting powers and combinations exclusive to movies and promotions.
Misfits: Although most people were only given one power by the Storm, a drug dealer has the ability to transfer powers from one person to another. One of his customers bought telekinesis, walking on water, teleportation and the ability to drive people mad with lust when he touched them. Simon bought precognition, time-travel, and immunity to others' powers. In a few rare cases people gained secondary powers from the storm, such as Nathan gaining immortality and the ability to see the spirits of the dead, and Simon gaining invisibility and super-human aim.
In Haven, Duke Crocker (and by extension, the Crocker family line) absorbs a Troubled person's blood to gain Super Strength and have his eyes glow silver for about a minute. If he kills a Troubled person, everyone else in the victim's family is Brought Down to Normal.
The horse thing came from a story where Poseidon and Athena were challenged to come up with something both beautiful and practical by some settlers, who agreed to name their city after the winner — Athena came up with the olive tree, and Poseidon with the horse (the city in question is Athens, so you can probably guess who won). Another variant of the myth has Poseidon offering the city a less-handy (but decidedly more Poseidon-ish) saltwater spring. (The myth explains two natural features of Athens, the aforesaid spring and an olive grove supposedly predating the original settlement.) Which lends support to the Retcon idea.
A lot of such gods have justifications, that usually don't immediately make sense unless you were worshiping them at the time. For instance, Pallas Athena was the patron deity of Athens (obviously), and associated with defensive warfare, wisdom and olive trees- things primarily associated with Athens.
This also helps us date the myths. For instance, Athens was also known for its extensive sea trade (which included settling about half of the Greek colonies in Ionia), so this legend probably dates from a time when that association had been made (i.e. towards the end of the Greek Dark Age), and people were asking why they seemed to have favor with Poseidon (or somesuch).
The earthquakes are because the land was thought to float on the water, meaning that he could cause earthquakes without touching the land.
Artemis is the goddess of virginity and childbirth because when she was only minutes old she helped her mother Leto give birth to her brother Apollo. The goddess of the moon part started with the Romans who stopped worshiping Selene the moon goddess and gave her the name Luna Diana.
Catholic Saints and their Orthodox cousins carry on the tradition. St. Christopher, for example, is patron saint of bachelors, travelers, gardeners and toothache. Or traveling bachelor gardeners with toothaches.
St. Barbara is patron saint against death by artillery, and hatmakers. She is also the patron of the Strategic Rocket Forces.
Could be explained by her also being the patron saint of Miners. Miners need a good hat and (in newer times) protection against explosions.
St. Michael the Archangel is the patron saint of radiologists, soldiers, paramedics, paratroopers, police officers, communications workers, postal workers, grocers, supermarket workers, stevedores and longshoremen. Supermarket workers!
Saint Nicholas is one of the oldest examples. The saint who forms the base for the Santa Claus is the patron saint of sailors, merchants, archers, thieves, children, and students. If that mix wasn't enough, he is also considered the saint of prostitutes. Legend has it he saved three daughters of a poor man of a lifetime of prostitution by dropping money through the chimney, leading into the Saint Nicholas/Santa Claus legends.
Inari Okami, Shinto god of rice, agriculture, industry, worldly sucess (okay so far), fertility (sure, why not?) and...foxes? Also once revered as the patron god of blacksmiths and protector of warriors.
While there's no doubt Inari fits this trope ("worldly success" alone puts him in the realm of "damn near anything"), the foxes make sense. The general agreement is that foxes would sneak in and kill livestock or generally ruin farms, making them Inari's "enforcers." In other words, you mess with Inari or don't please him, and he'll send his foxes to ruin your farm (remember, he's a god of agriculture, he gives and he takes away.)
Name an Aztec deity. For instance, chief deity Tezcatlipoca was a trickster god whose domains included the north wind, darkness, chaos, rulership, discord, hurricanes, obsidian, jaguars, slaves, and beauty.
Superhero RPGs in which the characters are randomly generated tend to fall into this trope regularly, for obvious reasons.
Golden Heroes: an early Australian entry in the field, allowed the player to roll for random powers—but then required her to come up with a justification for all the powers working together. Any powers the GM wasn't convinced were properly explained got cut.
Super Munchkin: your powers are literally based on the luck of the draw.
Nobilis: while some Imperators have reasonably connected purviews, such as 'Lucifer, Imperator of Pride and Persuasion', you get others like 'Askelon, Imperator of Tremors, the Culinary Arts, and the Forge', or 'Ananda, Imperator of Murder, the Infinite, and the Fourth Age'.
Stuperpowers will often have player-characters who end up with a completely random and unrelated set of abilities. Given that humor is the order of the game, "conventional" superpowers aren't available to players, and the characters are supposed to be playing really lame/obscure superheroes anyway, this is perhaps to be expected.
The Tane of Pathfinder all have this going on, reflecting both Bizarre Alien Biology and their origins. The Jabberwock has "eyes of flame", the "whiffling" of its wings creates a small windstorm, and it can "burble" to confuse or kill opponents. The Bandersnatch has quills that cause extreme pain, can drive a person mad with a stare, and is a superb tracker, and some types are "frumious" and set themselves on fire when angered. The Jubjub Bird adapts to attacks, has a stunning screech, and its bite is a One-Hit KO.
City of Heroes and City of Villains:other than epic archetypes, there are restrictions on what powers are available to their chosen archetype, but little restriction to the combination of those powers. Any primary power set can be combined with any secondary powerset, making a character who is Fire/Fire just as likely as one who is Fire/Ice or Ice/Fire. Some sets don't have a counterpart at all, like Poison and Force Fields, so they will be seen combined with just about anything. Using non-matching sets often results in more powerful characters due to metagame synergies.
And that's just at creation. Starting after level 41, you can get Ancillary power pools based on your class but again otherwise unbound (so a Tanker with a shield in one hand and an axe in the other could suddenly start throwing out fireballs, or develop psychic/energy shields, etc.) The villain equivalent that you need to run a mission to get are Patron pools, which are thematically bound to said patron (though running the quest for one unlocks for all) but otherwise unique. And that's not even getting into Incarnate abilities...
Mario: The title character has had a long list of powerups along the years, among them: A Super powerful Hammer, power to shoot fireballs, to grow in size, temporary invincibility, a flying raccoon suit that transformed into a statue, a Frog suit to swim faster, a turtle suit that gives him an infinite supply of hammers, a giant clockwork boot, a pet Dinosaur to ride on, a Flying cape (which deflects projectiles in Super Smash Bros Melee and Brawl), rabbit ears that allow him to Glide and Super Jump, hats that let him become solid Metal, Intangible/Invisible, or Fly, the ability to puff himself up like a balloon, a water gun that straps to his back, and the latest game gave him Ice powers, and Ghost, Bee, and spring transformations. Not to mention his vanilla standard powers of Super jumping, Super Speed, and Super Strength that he always has. New Super Mario Bros. Wii adds a Penguin suit that can swim like the Frog Suit, toss freezing snowballs like the Ice Flower, and walk on ice without slipping. And the Propeller Hat for flying. Plus has the Mini Mario from the DS game that is super tiny and can run across water without sinking.
Wario in the Wario Land series. His transformations range from the somewhat normal (on fire, flat, etc) to somewhat odd (become a vampire, zombie, invisible, frozen) to the completely insane (head puffs up like a balloon to float to various areas, dizzy/drunk Wario in Wario Land 3 and the weird hats in the first game allowing a head mounted jetpack or flamethrower).
If Shepard asks Thane about his beliefs in Mass Effect 2, one of the deities Thane reveals he prays to is Kalahira, Goddess of Oceans and the Afterlife.
Shepard: Oceans and Afterlife don't seem to have much in common.
Thane: Consider. The ocean is full of life. Yet it is not life as you and I know it. To survive there, we must release our hold on land. Accept a new way to live. So it is with the death. The soul must accept its departure from the body. If it can't, it will be lost.
All over the place in Tales of Rebirth. Veigue can create ice at will but he has no control over even the related elements, like water. Eugene has power over metal, which understandably incorporates metallic meteors and possibly electricity (electromagnetism?) but doesn't explain how he can generate small tornadoes. Tytree, on the other hand, has control over plant life, which somehow encompasses creating tiny earthquakes and geysers. And these are among the least unusual examples. Since it's a very action-heavy game, there's no real justification for these mixtures other than Rule of Cool.
Yukari Yakumo from Touhou has the ability to manipulate boundaries, usually manifesting as portals to an eye-filled dimension. However, "boundaries" is so vaguely defined it pretty much boils down to "can do whatever she wants" like manipulating the boundary between youth and old age, life and death, reality and imagination... Thankfully, she only uses her powers to troll people, assuming she even gets out of bed.
Corvo and Daud from Dishonored are both touched by The Outsider and have a grab-bag of powers as a result: teleportation, enhanced agility, the ability to summon rats, the ability to turn corpses to ash and so on.
Tao: a genetically-engineered "perfect weapon", has heightened agility, strength, and stamina. She is also immune to intense temperatures, being able to survive naked in both the jungle and the arctic tundra, can eat nearly any sort of organic matter, is immune to poisons, and can hold her breath for hours.
Tennyo: keeps finding new things she can do. Flight, ability to ignore gravity and inertia, super-strength, the ability to move through force fields, the ability to produce some form of antimatter, the ability to cast spheres of plasma, the ability to heal frighteningly fast from incredible injuries, the ability to form some sort of plasma "light saber", resistance to temperature extremes, she doesn't need to breathe air, etc. She also has thrown some sort of energy ball that temporarily acted like a neutron star, she may be able to teleport (although she was unconscious at the time), she may give off deadly levels of radiation when she's straining hard in a fight, and in one battle against over a hundred armed badguys, she literally warped reality all around her and opened up a rift in space-time. Oh, and she may be the avatar of some extra-terrestrial or extra-dimensional demon. We don't know yet.
Merry: who started out as a combination energizer/technopath (reasonable so far), then got roped into a secret church order and endowed with mystical powers (notably the ability to heal herself or others with the side effect of sending her own soul to Hell for a brief visit), and the incident that permanently split her up into Petra and Paige (with two personalities each — it's a bit complicated, okay?) also turned the latter into a werecat...
Murphy: powers allow her to warp reality, grow back limbs, and cause dead animals to follow her around.
Trinton Chronicles: every character has between 2 and 6 powers normally; in some cases these powers don't seem to belong to the same person!
Sabella: Generates electricity, controls water, and is empathic.
Robert: Can manipulate magnetic fields and summons other worldy beings.
Brandon: Has innate understanding of machines by touch and portal creation, his understanding of machines allows him to create objects that can boost his own power of portal creation or expand the range of other's powers.
Aurora: Is capable of creating energy clones, creates objects, induces living dreams/nightmares, can dream-walk, and is tied to the Astral Plane in some fashion.
Dan: Has power over time and generates dark and light energies.
Coatl: Is able to heal by touch and boost the powers of others at will.
It's also revealed that, with time, all of them can learn how to teleport, though only Will ever uses this.
South Park episode "Good Times With Weapons": parodied extremely well.
Cartman: Hold on you guys. I actually have another power. I can see into the future too, but better than Kyle. Let me try it. Kyle: Goddamnit, Cartman! You can't keep making up new powers! Stan: Yeah dude, that's like the fifth power you've come up with! Cartman: I am Bulrog and I have lots and lots of powers!
As of A Song Of Ass And Fire, Kenny has gained this, with both the Hyper-cuteness powers of a Magical Girl Japanese Princess, and his powers of self resurrection from his parents pact with Cthulu.