Essentially, Screw Destiny as a superpower.
A character is able to alter the laws of probability for a local area, resulting in "good luck" for them or "bad luck" for the opponent in the form of random and unlikely incidents happening spontaneously. The Dragon chasing you over a suspension bridge? Use this power, and the bridge's otherwise imperceptible design flaws will suddenly make themselves present, causing the bridge to collapse just as you make it across, but before your pursuer does. Need to stop a supercomputer from launching nuclear winter? This power will cause its state-of-the-art, Nobel-prize-winning software to crash spectacularly.
The only thing bad about it? Usually, you won't have any control over how probability is altered. You can have a specific outcome in mind, but there will always be a chance it won't work, or worse, turn against you at the worst possible time (namely, whenever you're about to save the day). Meaning your control over the forces of reality... well, y'know... isn't. This may mean that while the universe will look out for them on the big stuff (their survival, saving the world) they might be very unlucky in normal life.
This is for characters who can actively and consciously change the laws of probability in their area, or if such alterations would constitute a Necro Non Sequitur. Just having everything go your way is being Born Lucky. Keep that in mind when adding examples below.
In games, this kind of ability may be represented by a Luck Manipulation Mechanic.
Because almost everything theoretically has a chance of happening, when cranked high enough this power begins to overlap with Reality Warping. When this power lacks punch on the other hand, it can easily slide into What Kind of Lame Power Is Heart, Anyway?. Sometimes it even alternates between the two and sometimes it can be both. Immune to Fate is related to this trope in a sense * Both are defined as Screw Destiny as a super power, but this trope is more about actively screwing Destiny, while Immune to Fate is about one person passively being able to Screw Destiny, but not completely comparable. Some interpretations or inversions of this power could be related to Doom Magnet.
Has nothing to do with They Changed It, Now It Sucks. Although that would make for a good laconic description. That might be a bit too meta, however.
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Anime and Manga
In Bleach, Moe Shishigawara has a luck-based Fullbring. He boosts up his own luck, while bringing bad luck to others.
Well, if it came down to defeating the entity that wants to destroy the universe, or keeping a promise that you made and just forgot due to death and rebirth (and fixing mistakes that you yourself made), what would you do?
As an inversion of the trope, Himawari from Xxx HO Li C randomly causes bad luck to anyone who tries to become close to her, with the exception of few people: her parents and Doumeki. She can't control when it happens or who to.
The Vision of Escaflowne. The primary antagonists have a machine that can alter someone's fate. Played most straight with the "Intensified Luck Soldiers" Naria and Eirya, who get powered up with "lucky blood" which causes, among other things, lasers fired at them to bend off-course, swords swung at them to veer dramatically off to the side and flying mechs persuing them to spontaneously power-off and drop out of the sky. Unfortunately for the two of them, that blood proves to be Power at a Price. Also, the antagonists' power doesn't work well around Hitomi—she has such a strong sense of belief in a world of Clap If You Believe that she's unconsciously trumping them.
Amae Koromo of Saki. There are Born Lucky players who could get the Mahjong tiles they need almost all the time... and then there's her. She's not only Born Lucky, she can actually manipulate the luck of everyone around her so that no one else on the table could ever get a good hand unless she lets them.
Also, the titular heroine, Miyanaga Saki, who is quite clearly described by her to-be teammates in the first episode as having "superhuman luck" as if it were an actual superpower. Then again, considering the kind of ridiculous hands these people get, it probably is.
This is the power of Ania Fortuna of Asura Cryin'. As a luck eater, she can remove or add to the luck of a person in the area by biting them. The uses for this are variable, from giving Tomoharu an edge in battle to making sure he's on the receiving end of pranks.
Horribly deconstructed in the first Tokyo Babylon OAV. Shinji Nagumo noticed he had suchan extremely good luck that he survived several accidents: he became so smug that he actually started to set different accidents involving him and his work rivals/superiors. . . so that he'd as much get small wounds, but the others would end up dead. I.e., he tampers with an elevator which falls down its hole with him and the head of the enterprise inside then stops mid-fall; as a result, Nagumo gets a broken arm and the old man dies of a heart attack, setting Nagumo as a possible successor to his director seat. Too bad the boss had hired Subaru Sumeragi believing that there was a curse in his company, so this puts Subaru and Seishirou in the case...
This is a good way to look at the Zero System in Mobile Suit Gundam Wing, which can show someone all the thousands of different ways a battle can go and enable one to see the scenarios where they win. Trouble is, getting all that information thrown at you all at once tends to Mind Rape the inexperienced. Zechs and the Gundam pilots each had breakdowns when they encountered the system for the first time, and it took time, some guts, and the right situation for each pilot to find a way to make sense of the system.
In Tengen Toppa Gurren Lagann, the Anti-Spirals have access to missiles that alter probability to prevent the targets from avoiding or blocking them. This technology is thrown right back at them in the final battle; missiles that can't miss happen to be perfect for Attenborough's favouritetactic.
If he could control it, this would be what Touma, from A Certain Magical Index, would have. He essentially suffers from unbelievable bad luck with Power Incontinence. This has a hidden advantage, however: He's so unlucky that his right hand has the ability to literally block any Psychic Power it comes into contact with by cancelling out the user's luck as well.
The villain One-Eyed Othinus, aka Odin, has the ability to have a 50/50 chance of success at anything she tries. However, she has no control over it, meaning she has a 50% chance of giving her foe a Curb-Stomp Battle no matter how powerful they are or a 50% chance of losing to a wimp. Because Touma has very bad luck, when he faces her, she almost always gets the 50% chance of victory. She seeks the sacred spear Gungnir, so she will be able to control her ability and get a 100% chance of victory.
The main character in Psycho Busters appears to have this, with things like pieces of the ceiling falling to intercept attacks or the floor collapsing under his opponents feet just before they attack. It turns out to be just highly precise subconscious time manipulation.
Mawaru-Penguindrum's fifteenth episode reveals that Momoka's diary has the ability to change fate in exchange for something important to the user.
In Magi - Labyrinth of Magic, the black Rukh grant the ability to alter destiny. The villains even come close to repeating the trope name verbatim when invoking the black Rukh power in the Balbadd arc. Later revealed to be an inversion. People already have the power to Screw Destiny since the White Rukh embodies Free Will. Black Rukh embodies destiny, and accepting its power means surrendering self-determination. This inevitably leads to suffering and death since that is what the entity that produces Black Rukh wants.
JoJo's Bizarre Adventure Part 7 has an odd version in Pocoloco's stand. Instead of changing luck itself, it just whispers commands for him to follow, to make the most of his already rather sizeable luck, driving it from passable to ridiculously lucky.
Much later we have Valentine's Love Train, which allows him to redirect any misfortune aimed at him, such as physical damage, elsewhere across the world.
Kanojo ga Flag o Oraretara: Souta has the ability to see flags on top of people's heads, allowing him to see and change important events and choices in life. He can also break flags by taking action to prevent events he doesn't want to happen. He's not up on all the nuances, however, particularly when it comes to the way his friends' flags appear (or don't). Mei had a lesser form of the ability before she lost her memory.
In Toriko, Ichiryuu's main ability, Negative World, is a passive and simple version of probability manipulation: He inverts chance. He uses it in combination with techniques with a Million to One Chance—under Negative World's effect, it becomes an almost guaranteed outcome. This backfires on him spectacularly when his opponent catches on and not only tries unlikely moves of his own, but because Ichiryuu almost guaranteed death on his opponent—under normal circumstances—Negative World allowed him to keep living long enough to kill Ichiryuu.
Spider-Man's Black Cat had the (latent) mutant ability to cause "bad luck" to anyone who threatened her or her friends, with the unfortunate side effect of giving her friends rotten luck, as well.
Also, when initially introduced, part of her schtick during a robbery was setting things up beforehand so that it would seem that those who chased her were falling prey to completely random acts of God.
In The DCU, the super-villainess Hazard causes bad luck for her opponents by tossing a pair of dice (that always come up snake-eyes).
In The DCU, villain/hero/villain again/hero again Major Disaster's probability-altering powers allow him to cause apparently anything that can be labeled a "disaster" e.g. earthquakes, meteor showers, power outages, heart attacks, etc. Not to mention an "entropy shield" that causes bullets and such to miss him.
Talisman from the Justice Machine comics had this power. One standard tactic of the team (much to Talisman's disgust) was to throw Talisman towards their enemies. This would in variably result in the bad guys guns jamming as they attempted to shoot Talisman.
Longshot from the X-Men has this ability, though it's magical and not a mutant power. Further, it has a catch that he can't use it for selfish gain. Defending himself is fine, but no trips to Vegas. The villainess Roulette also had this power, her psychic energy manifesting as red chips for good luck and black chips for bad. Domino is often cited as well, but her powers are more Born Lucky than this trope, since she doesn't directly control what happens.
In the "Ultraheroes" Affectionate Parody of superheroes story running in Walt Disney's Comics #701, Gladstone Gander, already Born Lucky, is upgraded to the ultrahero "Cloverleaf" with this power. He then engages the also upgraded Pegleg Pete in a Curbstomp Battle. At least until Pete's dogged determination to keep on fighting despite how badly outmatched he was engaged the crowd's tendency to root for the underdog. Since Cloverleaf's motivation for heroic acts is to gain favorable public attention, he wished he were on the losing end—and his powers instantly fulfilled that desire.
Shamrock (Marvel's attempt at an Irish Captain Ethnic) is somewhere between this and Born Lucky. She's accompanied by ghosts that manipulate events in her favor in return for her helping them resolve Unfinished Business. Note that this isn't always a good thing—her fight with Deadpool in Marvel Zombieswent the same way as the Ultraheroes example above, when Deadpool convinced her that death was preferable to living on in a ruined world.
Amadeus Cho is eventually revealed to have a variation of this power. When sufficiently charged up (usually via sugar), he can actually see the formulae of event probability, and pick or dismiss which ones he wants to happen or doesn't, essentially setting off Rube Goldberg Devices of reality warping. Especially fun when he uses it on telepathic opponents, as they can also see what he's doing, but most can't duplicate or even keep up with it.
In Tangled, the song that invokes the flower and later the hair calls on this.
Heal what has been hurt Change the Fates' design Save what has been lost Bring back what once was mine
The Ta'veren from The Wheel of Time series have this to varying degrees (which also varies arbitrarily over time), but they have absolutely no control over it and no way to turn it off. Things can get really weird across an entire city around them at times.
Moreover, the same power in fact pushes them (and those around them) towards their destinies, for better or worse. Not so much Screw Destiny as a superpower as You Can't Fight Fate.
The power seems to have specific effects for each of the ta'veren. Mat's power seems to directly tweak probability, one time actually rolling a perfect roll with a set of dice weighted to land slightly lower than a perfect roll. Perrin's seems to tweak people, making them say or do things they wouldn't normally do. And Rand just causes everything in a very wide area to go haywire just by being there long enough.
Late in the series, there are signs that ta'veren can have some control of their power and literally twist the Pattern of Ages to their will. Rand starts threatening to will people to death, and though he doesn't actually do it, it's treated as a real possibility. And it may also counter the Dark One's taint on the land itself. For example - it appears that all the foodstuffs in a ship's hold are rotten. Until Rand shows up and the bags opened from there on out are fine. They just happened to check only the rotten ones before.
This seems to have something to do with the ta'veren's intent. When Rand is despairing and verging on destroying the world himself, he stops causing any good events, only bad ones. After he gets some Epiphany Therapy, the opposite seems to happen.
Aornis Hades from the Thursday Next series had the latent ability to cause extremely unlikely misfortunes: being struck by lightning, or being crushed by a car jettisoned from a zeppelin. This is explained as some sort of entropy manipulation. It causes all manner of bizarre coincidences beforehand that can tip off the intended victim, but that's only useful if you know about it.
It can even be used in your favor: Thursday at one point tries to find a certain person's telephone number, but the phone book lists more than 50 people with that name. She just pierces the page with a pencil right before leaping out of the way of a car - and, of course the pencil hit the right one.
As explained in the appendixes of the The Death Gate Cycle, Patryn and Sartan magic is based on modifying probabilities so that the outcome you want happens, instead of what was most likely to happen.
The magic in C. J. Cherryh's Sword of Knowledge books consists entirely of causing the target to have good or bad luck.
Beowulf himself says, "Fate often saves an undoomed man, if his courage is good." Implying that most anyone can alter their own fate by their actions... but if you're doomed you're doomed.
The main character, Bink, in the first Xanth book ''A Spell for Chameleon" had a magical ability never to be harmed by magic; he had no control of this power and the power always managed to make it look like his survival was purely by chance so for a long time everyone assumed Bink had no magic ability at all. The rationale for this subtlety seemed to be that if Bink's enemies knew he was invulnerable to magic they would use non-magical means to harm him, so his own magic talent kept itself hidden. But considering that any method of discovering his talent would be magical, and therefore influenced by his talent, this may be a slight Plot Hole (or not - not all means of finding things out are magical, just the most convenient ones).
Later books seemed to indicate that Bink's power grew from just protecting him from magic, to making him the luckiest person to ever live. Some characters speculate that his powers actually managed to manipulate the True NeutralEldritch Abomination that serves as Xanth's God and source of all magic, and that his luck also partially protects his many descendants as well. Essentially, Bink's power is unconsciously causing the universe to play Gambit Roulette in his favor.
Magician Murphy's magical talent also in the Xanth series: "Anything that can go wrong, will go wrong." Unfortunately, while he can control the end result he is seeking, he cannot control what will go wrong in order to make that happen. Initially he uses it for himself, but later uses it on another's behalf (causing the other person's enemies to suffer). His Heel-Face Turn basically came when he had to invoke his talent on behalf of his son, Grey, who was drawn to Xanth on his own and about to be forced to serve the morally-ambiguous Com Pewter—the curse worked when Grey became an apprentice under Good Magician Humphrey, whose obligations trump anyone else's.
In Night Watch novels by Lukyanenko curses on people result in an attraction of bad luck to that person. Cursing is an ability even normal people can do - and is why the Light Others are so careful about swearing about someone doing something.
The Others can also look at their "probability threads", their possible fates in the next few hours and pick their paths accordingly. A conscious and inverted version of this trope, if you will.
In The Dresden Files, several villains can cast "entropy curses" which cause their targets to suffer convenient accidental deaths. Exactly what kind of accidental death is heavily influenced by who's casting the curse; when the caster has a practical, organized personality, the "accidents" are simple and unremarkable, but when cast by someone undisciplined and prone to dramatics, the curses tend to result in things like the target getting hit by a car... while water skiing. Or someone being crushed by a frozen turkey which fell out of an airplane. (The temperature sensor then popped while everyone was staring at the crushed body, resulting in a Crowning Moment of Funny in the middle of a fight scene.) To a lesser extent, all wizards are stated to have this going on all the time - it's how the Magic Versus Science thing works. Just by being near a complicated machine, a wizard makes random errors more likely to occur.
Justified the hell out of in Greg Egan's novel Quarantine. Something involving quantum mechanics, wavefunction collapse, and an "eigenstate mod." I could try to explain it more, but we'd just both end up confused. Unfortunately, since this particular gift is distributed as a body modification, chaos breaks out when a city's inhabitants receive the mod: almost every single citizen temporarily becomes a Reality Warper, and though the rest of the world is apparently unaffected, Reality Is Still Out To Lunch in that particular city.
The Lazy Guns from Iain Banks' Against a Dark Background worked by causing a unlikely event when you pulled the trigger on someone: instead of simply being shot, an anchor might fall on them and kill them. If shot at a ship, a tidal wave could destroy it.
In Tanya Huff's Keepers Chronicles series, the Keepers have the ability to alter reality by changing the probability that certain actions can or will occur. For example, the heroine can take her familiar, a talking cat, into a restaurant to eat by changing the probabilities that anyone inside the restaurant will notice anything out of the ordinary. Or, she can get a noisome person to vacate her presence by increasing the probability that they need to get to the nearest toilet, immediately.
Fitz, from Robin Hobb's Farseer and Tawny Man trilogies, is a Catalyst. A Catalyst is periodically born in conjunction with a White Prophet who can see possible futures. The Catalyst alters circumstances just by existing, causing the possible futures the Prophet can see to multiply and better enable him to guide the world down the right path.
The titular protagonist from Leven Thumps is an offing, which means he has both the power to see a bit into the future and manipulate it, although he cannot always control how he manipulates it.
The Chaos Weapon by Colin Kapp is a Wave Motion Gun with this capability: if something bad will ever happen in the target area, the Chaos Weapon can make it happen NOW. Lightning strikes, dams giving way, earthquakes.... And at least some of the power needed to move the event from its proper place in space-time winds up increasing the violence of the event.
In Wolfgang Hohlbein's Die Rückkehr der Zauberer (Return of the Sorcerers) having luck is the protagonists main ability. Examples of use are him finding a pack of zigarettes, manipulating cards (making him always predict the wrong card), or turning all traffic lights green when he drives with over 60 mph through the city.
Luna of the Alex Verus series suffers a curse that causes her to essentially steal luck from those around her, causing misfortune to anyone who crosses her path in exchange for being essentially immune to random accidents herself. If that sounds handy, that's because it's actually a variant on a defensive spell: The curse is that she can't turn it off, making long-term relationships extremely difficult.
Harry Potter gives us a potion called Felix Felicis, a potion which will make a person phenomenally, impossibly lucky. There is no chance of "Felix" screwing up and almost everything will go right for the user. In fact, it's not even limited to mere probability, as Harry actually goes out of his way to do something that was not his plan simply because it felt like it was the right thing to do, and it worked. In fact, it is wizarding law that one cannot use it whenever they're supposed to be making a bet, have a Quidditch, are taking a test, etc. The drawback comes in that it is a dangerously tricky potion to make and it is dangerous to use it more than very sparingly. Also it is stated that luck can't do everything, as we find out in the end of book six. The tie in book, Fantastic Beasts and Where to Find Them, gives us the exact opposite of Felix with the Mackled Malaclaw. It has a venom which will make the victim impossibly unlucky, and the book even warns that a victim should cancel any bets, duels, tests, etc. as they are sure to go against the victim.
Voldemort (Tom Riddle at the time), puts a curse on the Defense of the Dark Arts position that makes it impossible for any teacher to hold it for more than a year. Judging by the nasty fates that tend to befall said teachers, it may also curse their lives as well.
In Larry Niven's Ringworld series, it's established early on that the Piersens' Puppeteers had been breeding humankind for pure dumb luck. When Nessus attempts to recruit one of the more lucky members of the species in order to improve the odds of their mission, all of the candidates just happen to be on vacation or are having communication glitches or are simply impossible to locate. Only one of these people is found and, unfortunately, her luck is more centered around her living a full life rather than being centered around her remaining comfortable and content, ultimately leading to the events in the book.
Not only is she lucky, she's descended from a line of people who were only born because their parents were lucky enough to win the birthright lottery for several generations.
Quite a few of powerful beings in Nightside have a form of this as a power. King of Skin knows your biggest fears and can alter reality to make them appear right here, right now. Count Video rewrites history by choosing and enforcing an alternative time track. Count Entropy and later his son could pick and choose any Million to One Chance in anything and make it a dominant one.
In the Rainbow Magic series, Lindsay the Luck Fairy has good luck powers.
Live Action TV
Trance from Andromeda has the power of luck, and if made to guess, will usually guess correctly despite extraordinary odds. Also, her presence might cover what in other TV shows is taken for granted: none of the main characters die, and the Andromeda doesn't explode.
In a later episode, it turns out that she actually is able to see the multitude divergent futures and follow them through to where the main characters don't die. It gets really burdensome on her.
The leprechauns of Charmed can bestow good or bad luck on someone. The episode "Lucky Charmed" involves a demon who is threatening the community of leprechauns, and ends with this demon getting hit by a meteor.
In Red Dwarf, this power is bestowed upon anyone who contracts the good luck virus. Lister uses it twice in the series to perform such feats as finding discarded fully functional weapons and correctly guessing a security password on his first try.
In the Star Trek: Deep Space Nine episode "Rivals," the central guest character obtains a device from a dying alien that allows probability to be altered. He then somehow manages to create larger versions, which then go on to wreak havoc throughout the station. When the crew figure out what's going on, they destroy the devices, which are then never heard of again.
An episode of Supernatural revolved around a rabbit's foot that was stolen from one of John's storage units. The foot would bestow great luck on its owner...until they lost it, after which their luck would be nothing but awful. Death was soon to follow.
And it was hilarious. Poor Sam.
This is one of the ways The Force can manifest itself in the Star Wars universe. Sometimes directly, as in the example above from the Knights of the Old Republic comic, with a character who warps chance. Sometimes indirectly, as with Anakin in The Phantom Menace, who appeared to be a much better pod-racer than he actually was because he could see the future. Sometimes very indirectly as the Force takes you toward your destiny, willing or no. And, in a very meta way, this is what the Dark Side of the Force is. The Force is Space Daoism, and the Light Side means living in harmony with the Force, following its plan for the galaxy. The Dark Side means living out of harmony, opposing the will of the Force and instead forcing it to your own will. So, by the Lucas definition, every Sith lord is actively using this trope.
Changeling: The Lost has the Contracts of Hearth, powers that affect a person's luck with the caveat that they can't be used too much. The caveat responds to the magnitude of the power — a power that impedes another person can't be used on them more than once per day, a power that blesses another person's action can't be used for the exact same purpose twice per day, and a power that grants a truly monumental success can't be used more than once per year. Attempts to go against these provisions backfire. Badly.
Vampire: The Requiem has the Bohagande bloodline, with the power to steal others' luck for their own use.
According to some supplemental material the Lovecraftian god Nyarlathotep seems to have the ability to tweak probabilities to go to his favor, although it only seems to apply to small-scale stuff. His real power is being a Shape ShifterChessmaster (and, you know, a god).
In both Warhammer universes, Tzeentch, the god of Gambit Roulette, has it as part of his portfolio. There is a reason his greater demons are called "Lords of Change".
In Warhammer 40,000, the lowest-level psykers have a great deal of good luck. Higher-level ones may be able to influence it. The new Psychic Power Charts contain Divination, which has several abilities that cause this, such as "Misfortune" which causes an enemy to re-roll successful saves, and "Prescience", which enables a friendly unit to receive re-rolls to hit, which are similar to the Eldar powers, "Doom" and "Guide". In short, one of the best psychic tricks, is screwing destiny.
Complete Scoundrel gave luck feats and even a prestige class based upon them to Dungeons & Dragons.
There's also the Fatespinner (Song and Silence, later updated in Complete Arcane) and Luckstealer (Races of the Wild) prestige classes for spellcasters that like to manipulate fate.
For the gods in Deities and Demigods, the salient divine ability "Power of Luck" is basically this trope, and its strength is proportional to how many divine ranks the deity has.note Having more than 20 divine ranks in D&D is tantamount to being one of the Powers That Be.
In the 1st Edition Forgotten Realms boxed campaign set, Beshaba is the deity of Mischief, Misfortune, Ill Luck and Accidents. Surefire plans go awry, stout weapons or walls suddenly give way, and freak accidents occur to man and beast in places where she has been.
Magic in the Maelstrom gaming system worked by warping probability in this way. There were different grades of spells, ranging from "likely" through "unlikely" and "wildly improbable" to "completely impossible."
The original 1980's Marvel Superheroes RPG had the power of "Luck" - in a game where everything was determined by percentile dice, this allowed the character to ALWAYS take the higher die as the 'tens' digit, making it INORDINATELY powerful to have.
Mutants & Masterminds, 2nd Edition has Probability Control, a power which sets the minimum result of a roll equal to the number of ranks you have in it. It's possible to have 20 ranks in it... though it's expensive as hell. In addition, 20s produced this way are not criticals.
There's also Luck Control, a power that allows you to use Hero Points (usually spent to boost yourself) to help others, force others to reroll and take the worst of the two rolls, or cancel out "GM Fiat." This is usually combined with the feat Lucky to gain bonus starting Hero Points every adventure.
There is some debate over which of the two is better at manipulating fate. Probability Controll is more reliable and easier to use, but it cannot be used to make things worse for your enemies or cancel out a GM's "cause I said so". A lot of players solve the debate by taking both and make screwing the Dice Lords their main strategy.
Exalted: The very act of channeling Virtue is exactly this. And then in the Sidereal manual, it's revealed that the very act of spending Essenceoverrides the power of the Loom of Fate, and the pattern spiders who maintain the Loom must rewrite destiny in accordance with the effect used or suffer causality errors. So the wind regularly blows for Essence users, the biggest of which are your player characters.
3e introduces the Getimian Exalted, whose internal anatomy has been replaced with their own personal Loom of Fate. Thanks to that, they can control their own fate, and disrupt the weave of Creation's Loom by unleashing fates they've created.
Magic: The Gathering has numerous cards that allow a player to partially stack, reshuffle, or otherwise manipulate either their or their opponent's deck. A classic example is Portent while Preordain makes decks draw what they need so consistently that it had to be banned in Modern.
This is essentially how most magick works in Unknown Armies - while some spells do allow for blatant violations of physics, most of it just changes the probability that something you do (like lying, or attacking, or trying to dodge a car) will succeed. Of particular note are Entropomancers, whose entire shtick is surrendering themselves to fate in exchange for the power to manipulate it, and the Ritual of Light, a very powerful spell which puts this ability in the hands of the players, allowing them to decide the outcomes of actions by vote instead of dice rolls.
Godlike has the Aces power, which gives good luck to your rolls, and Jinx, which gives bad luck to your enemies. Justified that both of these powers use up lots of Will, the fuel that makes your powers work. Run out of will and your powers stop working until you get some more. The Aces power can even be improved with the 'Flamboyant' extra, which makes your powers go off in very obvious ways.
The fate point mechanic in the Fate System (Spirit of the Century, The Dresden Files et al.) is by default this more on the player than the actual character level in that spending fate points lets players alter the outcome of dice rolls and establish narrative details for their characters' benefit, especially with an appropriate aspect to back them up, but doesn't necessarily reflect so much any specific distinct 'in-universe' power. However, as long as the ability doesn't need to be mechanically more powerful than other aspect invocations, simply picking an aspect like, say, "Implausible Luck" or "Weirdness Magnet" (they're freeform) is all the narrative excuse a character needs to embody this trope while the player's supply of fate points lasts...and as with any aspect, more can always be earned by allowing it to work against the character every so often, too.
Nell (and to a lesser extend, her little sister Rachel) has this as her power in Advance Wars; her units are naturally more likely to score extra damage, and her CO power takes it Up to Eleven, allowing such impossible feats as infantry taking out a platoon of Megatanks.
The "Super Luck" ability which some Pokémon have, which doubles the probability of their attacks making critical hits.
Related is the "Serene Grace" ability, which doubles the probability of secondary effects activating (like an attack with a chance to also inflict a status effect).
In Sid Meier’s Alpha Centauri, sufficiently advanced factions can armor their units with "probability sheaths" in a practical application of Probability Mechanics.
In Fallout, "Luck" is one of the seven Base Stats, with this exact effect on your personal actions. Taking the "Jinxed" perk would cause both you and everyone else to suffer far more critical failures and lower your Luck stat, Fallout 2 upped the ante with Pariah Dog, who drops your luck to 1 once he starts following you around. Since all of this can stack, creating a Jinxed character with 1 Luck and Pariah Dog as a pet can turn the PC into a walking disaster area.
Creating a character with 10 Luck (the maximum) and the Jinxed trait creates a PC who is a walking disaster area, but is never touched by it themselves. Angel walking through the valley of death style. This is awesome.
You'll still critically miss much more than without the Jinxed trait (not perk), but simply because a gang of enemies have more turns that you, they'll be bearing the brunt of the fails. As such, a good tactic is to go solo and NOT ATTACK while enemies lose their ammo, destroy their own weapons, and break their own limbs trying to attack you.
Fallout 3 and Fallout: New Vegas lessened the effects of luck considerably, but it does determine your success at winning casino games in the latter. Low-Luck Couriers can say goodbye to their caps (6 or less), while High-Luck Couriers will be banned from a casino in ten or fifteen minutes for winning too much.
Though in New Vegas, your Luck stat is described as not being probability manipulation, rather it's probability prediction (which is what professional gambling is based on in real life) hence House, the guy who could predict the Great War coming down to the day and owns New Vegas itself, has the max Luck stat of 10.
Kingdom of Loathing has the Black Cat familiar; which causes everything to go wrong for you. If you beat Bad Moon with this as your familiar every single fight, that difficulty level is permanently unlocked.
There is also the Black Cat Tonic which temporarily lets you spread bad luck to enemies; upping their fumble rate and never letting their critical.
Opposing that is the Ten-Leaf Clover. Whn you enter an area with a Clover, it initiates a Clover Adventure if there is one in that area. Clover Adventures provide very good items, buffs, or stat points.
Milfeulle Sakuraba has what could be considered an unconscious version of this trope, only turned Up to Eleven. When her luck is good, it's insanely good (for example, her Establishing Character Moment in the first game has her winning the grand prize in a convenience store lottery five times in a row); however, when her luck is bad, it's horribly bad (a picnic being ruined due to a fire alarm being tripped, followed by the Cool Ship she and her crewmates serve abord warping out in the middle of an enemy fleet, followed still by her personal starfighter's engine crapping out on her). Her luck is also apparently finite, since it is said that she used all her life's worth of good luck to alter the outcome of the first game's Final Battle. Of course, the release of the sequels seemingly retcon that piece of information.
Just to hammer the point home, her craft, GA-001 Lucky Star, is explicitly said to be otherwise unsuitable to be piloted due to its engines, powerplant and even weaponry having unpredictable output. Only Milfeulle's sheer luck keeps it running, and running constantly.
Touhou has this as either an explicit or implicit superpower of several characters:
The HeroineReimu Hakurei implicitly uses this as her ultimate power - in spite of technically being totally outclassed in terms of raw power to the actual deities or Reality Warper enemies she fights, she uses her "Intuition" to frequently evade all harm from things that should flatten her to a paste. Of course, her explicit power is "merely" a low-level Reality Warper power, which may certainly help in this regard.
Remilia Scarlet has "Manipulation of Fate" as a (largely undefined) superpower, although she generally just uses brute vampiric strength in combat. It is implied, however, that she can manipulate destiny to ensure such things as the survival of her human friends, or the success of the machinations of the absurdly involved Batman Gambit plots of the likes of Yukari. It's unclear if she even knows she has this power, and if it is conscious or unconsciously used. One in-story rumour says she changed the fate of her maid by giving her a different name.
Both Hina Kageyama and Suwako Moriya are curse goddesses. Hina is a goddess of misfortune that can inflict bad luck upon people to the point where they suffer a Necro Non Sequitur. However, she generally likes people, and instead grants good fortune by eating the misfortune of others, if still dangerous due to her absolute lack of control over the accrued misfortune. Suwako gained curse god powers by bringing powerful curse gods under her control, but generally uses her powers to help others, largely because she needs people's faith in her to continue to exist, and as such grants good fortune and miracles in exchange for faith. Both, however, use their curse powers as weapons when in a fight.
And last but certainly not least is Tewi Inaba, the Earth rabbit youkai, who has the power to bestow good luck. She mostly uses it exclusively on herself, though.
In the Nasuverse, Marble Phantasm is the ability to interfere with probability to transfigure the surrounding world at will according to the user's vision of the world, limited to the scope of nature. The English name comes from a metaphor of picking a white marble from a bag of mostly black by making the chance of doing so 100%. In Tsukihime, Arcueid uses this to turn layers of the atmosphere in the corridor into a vacuum that shreds her target. (She was incapable of, for instance, distorting the floor.)
This is contrasted with the Reality Marble. A person with a Reality Marble would also have the ability to grab a white marble, by turning all the black marbles white. However, Reality Marbles tend to be limited to specific effects, as opposed to the Marble Phantasm's ability to basically do whatever the user pleases.
In Darths & Droids, one of the Jedi abilities is "fate manipulation", which, in game mechanics terms, allows a player to reroll a die. The characters use this to varying effectiveness throughout the games.
Although it takes a while for the ability to show up; it's first brought up as both a Take That and an I Thought It Meant when Qui-Gon uses this ability while convincing Watto to help with his simple plan.
In Erfworld, one type of caster is a Luckamancer. At one point a Luckamancer explains his magic by comparing units to dice. When one receives his boost, it only rolls max for the next combat it's in. But that luck comes from somewhere and he posits that it's from other nearby units. Even friendlies
In Homestuck, Vriska (after attaining god-tier) gains all of the luck. All of it. She literally has the ability to steal luck and cause misfortunes (such as a floor collapsing underneath her opponent), or to manipulate random events like coin flips in her favor. She's convinced that this makes her more powerful than any of her teammates and even the Big Bad of the comic, because it is impossibleforherto lose.
She can also weaponize this directly thanks to her weapon of choice being a set of enchanted d8 dice.
Clover of The Felt, a rival gang to The Midnight Crew, has luck that in theory makes him very difficult to hurt (he states that a gun pointed at him would jam). Diamonds Droog gets around this by swatting Clover with a newspaper — you don't have to be that unlucky to be swatted by a newspaper, it's kind of a grey area.
Although Cans, whose power is to be able to literally punch people into next week! Bursts in immediately. Yeah...
In Sluggy Freelance the Fate Spiders' ability to manipulate the Web of Fate is the inverse of how this power often works. They have incredible amounts of precision over which events they change the probability of, but how much they can alter probability is severely limited; they can only affect the outcome of events when the odds of one thing happening instead of something else are almost 50/50, like making someone decide to get pizza to eat instead of burgers. They have to make use of their immense knowledge of destiny and lots of For Want of a Nail moments to accomplish anything of significance, and even then someone who's Immune to Fate can still muck it up.
Domino is a slightly clairvoyant martial artist who can see the future just enough to let her avoid bad choices. Her teammates simply assume she's incredibly lucky.
Hazard, like Lady Luck, can manipulate probabilities directly. Unlike Lady Luck, he does so to commit crimes.
Several side characters in the webfiction Whateley Universe have this ability to some extent. Hazard (apparently a common name for these types of characters) also senses when unlikely events are about to happen, which is usually a sign to get the heck out of the area. Kismet has magical abilities and the ability to teleport short distances. When she teleports, local probability goes haywire: an opposing fighter is either going to slip on something or score an easy one-punch knockout. Risk likes to use his ability to play pranks and cheat at games like pinball. To say nothing of the cute little disaster that is Clover of the Three Little Witches (she's a wizard in the making all right, she just has this power on top of that).
The school's administration, incidentally, generally does its best to keep these 'probability warpers' separated — in different cottages, if possible — because of the risk of their powers heterodyning and spontaneously creating wholly unpredictable events.
The parahumans multiverse of Worm contains a number of straight up probability warpers, enough that it is a well known power set along with speedster and Alexandria package and others. Given the author's style no such simple version features in the story proper. Instead we see Shamrock who appears to have this power but in fact just has a whole host of smaller powers which effectively do the same thing and Coil, who can achieve this as one effect of his ability to view parallel dimensions simultaneously.
A member of the SCP Foundation's D-class personnel kept surviving experiments with Keter-class anomalies by seemingly impossible coincidences. Further experiments confirmed that he could influence probability, and he was designated SCP-181. Then it was found that his influence could cause [DATA EXPUNGED], so now he's in solitary confinement.
Discussed in several posts on Less Wrong, in the form of a device that takes a desired outcome and simply vetoes all possibilities that don't lead to it. The pitfalls are spectacular.
Jinx of Teen Titans has this as a power, although she's only capable of creating bad luck. Of course, this usually involves wanton spontaneous destruction.
Fry's lucky seven-leaf clover in Futurama bestowed incredible luck on its owner, allowing them to be immensely successful at anything they did. Maybe.
The Anti-Fairies in The Fairly OddParents are the complete opposite of fairies in the fact that they roam the world causing bad luck to people, reinforcing many popular superstitions such as spilling salt, walking under a ladder, breaking mirrors, etc. Unsurprisingly, their favorite day is Friday the 13th.
The black cat from the classic cartoon "Bad Luck Blackie" can cause random objects to fall on anyone whose path he crosses; he actually served as the inspiration for Black Cat's bad luck power (see above).
Toa Jaller has the Mask of Fate in his Inika form, which passively applies this to his physical actions. In practice, it acts as a Mask of Reflexes (of if you're feeling snarky, a Mask of Action Film Moves or perhaps a Mask of Take 20), allowing him to pull off theoretically-possible-but-extremely-unlikely stunts.
Toa Nikila has the Mask of Possibilities, which is closer to the spirit of the trope by the fact that it affects probabilities of events happening around the wearer.