Immune to Fate

“Some rare folk are what’s called fateless, ye see. They wander through their lives doing as they see fit, creating their own destinies. Ye have no fortune to tell, scarred one… none at all. I’ve nothing to tell ye… and so here is yer coin.”

—Fortuneteller returning her fee - Planescape: Torment

You Can't Fight Fate. Everything that happens, has happened, or ever will happen has been pre-ordained from the moment the universe came into being. No one can escape the inexorable tide of destiny.

Oh, except for that guy over there. Yeah, no way of telling what he's gonna do. Spanner in the Works is his job title. From the perspective of a Seer, he may as well be wearing a Kryptonite-Proof Suit.

Basically, every so often, a story will introduce a character who has the power to Screw Destiny as a special ability. Everyone else in their universe may be bound by fate, but all the prophecies you can conjure up don't mean squat if this person gets involved.

Examples of Immune to Fate include:

Anime and Manga

Ginji in GetBackers might be this. One thing for sure, not even Makube X could predict what he would do.
The Spiral Power in Tengen Toppa Gurren Lagann is, as Viral puts it, the "burning blood that cuts through Fate".
In Bleach Inoue Orihime's powers are introduced as barrier abilities that cut, heal and shield. As an Actual Pacifist she only heals and shields. Her powers are eventually revealed to Screw Destiny by rejecting events - injuries are rejected as ever having occurred rather than being healed. The catch is that her powers are limited by what she believes is possible or impossible and her pacifist nature. For a long time she thought restoring something that had been completely destroyed was impossible until shown she was mistaken. It was all she needed to be able to do it herself. She doesn't like seeing others hurt, so her ability to kill is weak and undeveloped (even her upgrade relies on turning her enemy's powers back on their source effectively making her enemy hurt himself).
In Vision of Escaflowne, the Big Bad is desperate to capture Escaflowne because it is the one thing his Fate Alteration Engine can't control the future of.
Sartorious from Yu-Gi-Oh! GX is basically fated to win any duel he enters, which automatically gives him the best of all possible outcomes in his very luck based deck. That is, until he met Jaden...
This is the ultimate goal of Guts (and the Skull Knight). After the events of the Eclipse, he has vowed to Screw Destiny and Rage Against the Heavens, occupied by the God Hand who control and use fate to their advantage. While he didn't die the day he was fated to (thanks to a combination of being improbably Badass and the timely intervention of the Skull Knight), he does not yet truly qualify for this trope as the Brand of Sacrifice is still trying (and failing) to "correct the mistake" fate made by drawing demons to him at night to kill him.
Pacifica Casull, a.k.a. the "Scrapped Princess", a.k.a. the Providence Breaker. She's actually genetically engineered to be Immune to Fate, and she manages to avoid the one fate she wasn't supposed to avoid.
Bellcross of Heroic Age's special power is "existence". He's punched his way out of a black hole he was trapped in, and was in one case attacked by a time traveler in tens of thousands of different timelines at various points. He survived in all of them.
Yukiteru Amano from Future Diary could not only change his own fate, but also others' fate.
An unusual variation of this exists in Ann Cassandra: Banjou is fated to die on his 20th birthday. Because there was a prediction of him dying on that specific day, he can't die before that day. This means that he can do all sorts of Leeroy Jenkins-style stunts without worrying about dying, as fate warps itself around him to keep him alive. Knowing this, Banjou uses his reality-warping presence to protect the lives of people fated to die, often by using himself as a human shield against whatever is about to kill that person. Given that Ann Cassandra is about teenagers who can see the future and want to stop terrible things from happening, this power is actually quite relevant most of the time. (The reason this isn't a straight example is because while he is immune to death, he is NOT immune to getting hurt, and he spends almost half of the entire series either in the hospital or with bandages on his body.)

Comic Books

Both Thanos of Titan and his good counterpart Adam Warlock have been remarked on as being outside the purview of Order and Chaos, and thus in some sense outside of fate.
- In Warlock's case this may be because he changed history by killing himself, thus preventing himself from becoming an evil god. He got better, though.
A recent reinterpretation of DC Comics' Challengers of the Unknown indicates they have this ability, a result of their living in "borrowed time" (they survived a fatal plane crash.)
In Flashpoint, Professor Zoom boasts to Barry Allen as being able to do this as he's a living Temporal Paradox. Batman/Thomas Wayne, promptly shoves a sword through his chest.

Fan Works

In DC Nation, this is broadly hinted to be something of a superpower for the otherwise Badass Normal Roy Harper. He's flipped off Cosmic Horrors and Jerkass Gods alike. In-universe, he is completely unreadable to Dr. Fate. At one point, Dark Angel is howling for his head, saying he should have died in Crisis on Infinite Earths. He shrugs it off.

Arsenal: "All you're telling me is that I've pissed in your Cheerios more than once, and I did it beside Donna. Lemme tell you, those are two things that make me a very happy little camper...And hey, extra bonus for me at the end of it? I pissed you off when I didn't even mean to! Little ol' me. A guy. A dude. A very attractive but semi-normal human fleshbag. Man, I'm good."

Mana Kirishima seems to have this power in Shinji and Warhammer 40 K. Nowhere in the prophecies does it mention anything about her, so when she gets Magnos Tancred and hence the actual ability to influence Angel-level fights, she can do things forbidden by them.
In the Veronica Mars meets Buffy the Vampire Slayer fanfic Martian Manhunter, Veronica is told (by Drusilla, of all people) that she has no fate or destiny that anyone can discern. Dru even explicitly makes the comparison to Sparhawk.

Literature

Sir Sparhawk, Champion of the Pandion Knights in David Eddings's The Elenium and The Tamuli series. The gods know him as 'Anakha', literally "without destiny", and most of them were in favor of simply not letting him get born. Because he has no fate, even the gods can't predict what he'll do from one moment to the next, making him able to actually fight them... in the end, the only reason they even allowed him to exist, is that sometimes, it's handy to have a godslayer around... providing they're careful where they point him.
- At the end of the second trilogy, it's revealed that he has this power - and more - due to being created by Bhelliom, the universe-transcending entity that created the world. Due to unwariness on its own part, it became trapped in the form of a gemstone, and 'created' Anakha to have the power to free it. Because he was created by something older than the gods themselves, they hold no power over him...
In the later Dune books by Frank Herbert, the God Emperor Leto II spends three and a half thousand years breeding humans to make a gene as widespread as possible that prevents prescient people from seeing what people with the gene are going to do.
Rincewind from Discworld, while in general being a Cosmic Plaything who can't fight fate, plays this specific role for Death. Due to Rincewind being favored by Lady Luck — Fate's arch-enemy — not even Death knows when he's going to die. (His hourglass has an... interesting shape.)
- More literally, there is Coin the Sourcerer from Sourcery - according to Death, Sourcerers make their own destiny. They touch the world lightly.
The entire Kender race (most notably, Tasselhoff Burrfoot) in the Dragonlance series, because they were created by mistake (as opposed to, say, Elves and Men).
- Specifically, Elves, Humans, and Ogres were created by the gods at the beginning to embody light, balance, and darkness, respectively. Kender, and related races such as dwarves and gnomes, were created by the Graygem, an Artifact of Doom containing the essence of pure Chaos. Needless to say, all three have the potential to massively screw up the timeline, with kender being the most likely to because they're naturally adventuresome and impulsive.
There is a Jewish legend about a sage meeting Death and asking him about when he's going to die. Death's answer? "Sorry, but sages as righteous as you get delays all the time".
Part of the job description of The Magids is being disentangled from fate... to a certain extent. While they are separated from human workings, Them Up There are free to meddle in their affairs.
Meta-example: in Kurt Vonnegut's Breakfast of Champions, Kilgore Trout writes a novel about a man who discovers he is the only free-willed being in the universe, which then causes an aged business magnate to go on a killing spree after believing this applies to him also. It doesn't.
Firekeeper, titular heroine of the Firekeeper series, is a human woman who has been Raised by Wolves. This causes her to have a chaotic nature such that skilled Seers, such as the Wise Jaguar, Truth, cannot accurately predict events she is directly involved in.
In Stephen King's Insomnia, people are defined by being born to the "Purpose" (important to the Multiverse in some way) and the "Random" (random extra as far as the greater Multiverse is concerned). Trouble brews when the Grim Reaper normally tasked with ending the lives of "Random" people cuts the lifeline of someone who isn't defined as "Purpose" or "Random". Main characters Ralph and Lois are conscripted by the "Purpose" Grim Reapers to prevent this act from screwing over the Multiverse.
Ilium and Olympos by Dan Simmons features as one of its main characters Achilles in an alternate timeline of the Trojan War. In it, Paris dies before he can kill Achilles, as the prophecy dictates. For the rest of the story, Achilles becomes immortal and indestructible, as his fate became impossible to bring about.
In Terry Pratchett's The Dark Side of the Sun, the Jokers are completely invisible to probability math, which can otherwise predict the future with near certainty.
In Terry Goodkind books, Richard typically says Screw Destiny, or rather claims he knows best despite wizards having studied them for years telling him otherwise. And somehow, he's always right, possibly because he's the hero.
It is stated in The Silmarillion that Men are free to make their own choices outside of the Great Music (i. e. Fate) while other races (Ainur, Elves, Dwarves etc.) have their Fates determined by it.

Live-Action TV

Time Travel on Lost follows, for the most part, the You Already Changed the Past model. The exception is Desmond, thanks to how the Island's electro-magnetism messed up his head. When he sees a vision of Charlie dying, he's able to prevent it, but has to keep on saving Charlie's life as destiny keeps finding new ways to off him. And when Daniel Faraday tells Desmond something in the past, present day Desmond shoots up in bed, suddenly remembering a conversation that, until just then, hadn't actually happened.
The Doctor from Doctor Who, Depending on the Writer.
- "The Waters of Mars", however, provides a particularly chilling Deconstruction of the trope.
Clark Kent in Smallville is implied to be this in the episode Hereafter.
- To clarify: There was a kid who could see the future (often seeing people's deaths) and became The Fatalist because nothing he did could alter his visions. His attitude changes when Clark rescues someone who he predicted would die, even though he had no knowledge of the vision and was just doing his regular superheroing since they hadn't even met yet.
- He also tells Clark that everyone is fated to die, but in Clark's future, all he saw was a cape fluttering in sea of stars.

Jordan Cross: You don't have an end like other people. It's like you live forever.

In Supernatural's fifth season, Sam and Dean are constantly told by the angels that, as the human vessels of Lucifer and Michael, they are fated to give in and that no matter how hard they try to avoid it, it's inevitably going to happen anyway. Sam eventually says yes to Lucifer, but Dean does not, forcing Michael to adopt their half-brother Adam Milligan as a makeshift vessel.
- To be fair, the angels are kinda dicks. They might well have been lying about fate.
  - It's revealed that they aren't just "kinda dicks" - a majority of them actively want the Apocalypse to go down, because they're tired of waiting for God to come back. They just assume that they'll win. Further, the angels have been known to try mindscrews and Jedi Truths if they think the boys will catch on to a blatant lie too quickly for it to be useful.
- In season six the brothers actually meet one of the Fates who is quite pissed at them for stopping the Apocalypse. The boys are apparently not literally Immune to Fate as she quite seriously threatens to kill them.
  - Because they are so entwined in Destiny the brothers seem mostly unaffected when Balthazar stops the Titanic from sinking and changes the timeline in a major way. The closer people and things are to the brothers and their destiny, the less affected are they by the changes.
In The Cape Dice is unable to see Vince in her predictions.

Tabletop Games

GURPS has the "Temporal Inertia" advantage, basically making a character immune to death by fate (among other things).
In Mage: The Awakening, mages with high levels of the Fate Arcanum become "Unfettered"; they are automatically able to detect and resist any attempt to magically alter their destiny, such as curses, attempts to bind their fate, mind control, or tampering with their soul. (On the other side of the coin, mages of the Mastigos path are terrified of mages with Fate, because Fate implies free will isn't all it's cracked up to be.)
- Mages reaching the apex of the Sphinx Legacy take this about a thousand steps further - they can "walk between" the patterns of the world, isolating themselves from it. They are literally immune to any magical attempt to alter, define or predict their destiny. Any attempt to use Sympathetic Magic on them automatically fails unless the caster knows their True Name. They even become extremely hard to pay attention to. However, by the same token, they disable one of their Legacy's other abilities, and are rendered practically unable to alter the destinies of anyone else, either.
Exalted has legions of these. The Underworld, the Wyld, Malfeas, and Autochthon are all outside Fate. (Autochthonians are the only ones who would feel at all guilty about disrupting Fate by walking in Creation - one charm submodule lets them become part of Fate just to avoid screwing things up. Everyone else considers it a job perk.)
Dungeons & Dragons features a fourth edition epic destiny for revenants called Free Soul with this as its schtick. You have won freedom from the goddess of fate, be it by arms or charms, and are now immune to the laws of death and destiny. It comes with nifty powers that pretty much let you roll saves as you see fit.

Video Games

The Fateless One in Kingdoms of Amalur: Reckoning. Seeing as how s/he starts the game off dead and comes back to life, there's a lot of ways s/he can break the world around him/her.
In the Legacy of Kain series, Raziel is essentially this trope. The only way to escape fate is to cause a paradox and take action right at the paradox, but Raziel is a spirit carrying his own spirit from a different time on his arm, so he's a paradox on legs, and everything he does alters history or, to put it another way, he's the only character who has real free will. However, being immune to the power of destiny does not make him immune to being manipulated in more conventional ways, and he spends a huge amount of the series as an Unwitting Pawn to various factions.
A book of background fluff in Baldur's Gate references a Forgotten Realms folk tale; when something is born the Goddess of bad luck calls a coin toss by the Goddess of good luck and the victor decides the newborn's fate, but sometimes the coin lands on edge...
- Both a Hermit in Baldur's Gate and a fortune teller in Baldur's Gate II tell the main character that their coin landed on the edge. The fortune teller also gives them a refund.
The Nameless One in Planescape: Torment. A fortune teller flat-out tells him as much, before giving him a full refund.
While he's at the very center of the maelstrom of fate in Chrono Cross, Serge seems to be astoundingly immune to being screwed by it. Crono from Chrono Trigger, not so much...
In The Legend of Spyro, the Purple Dragon is specifically said to be able to guide the fate of the era he/she is born into. Whenever someone predicts a destiny he doesn't like, Spyro tends to Screw Destiny. The Chronicler tells him that Cynder will turn evil again when Malefor is revived? He pulls a Big Damn Heroes moment and saves her while killing that particular game's Big Bad (though Word of God states that the Chronicler was aware Spyro may not go along with the future he fortold and taught him what he'd need anyway, it still counts). Malefor tells him the fate of the Purple Dragon is to destroy the world? He and Cynder kick Malefor's tail and Spyro restores the world.
A fortune teller in Seiken Densetsu 3 is shocked when he tries to tell the main character's future, and all he can see is a faerie. The Faerie then appears and says that, when she inhabits a human, his or her future becomes impossible to determine.
In Final Fantasy XIII, humans can transcend any kind of limitations, even their own fate. Fal'Cie, on the other hand, cannot: despite being infinitely more powerful than humans, they cannot act outside of very specific roles the Creator Deity assigned to them. Which is why they create l'Cie, in an attempt to control the fate-defying human will.
Certain background lore in The Elder Scrolls suggests that being a Hero is a limited version of this: you lose your ordinary fate (enough that a book supposed to tell you your future is blank), but are still restricted and controlled by forces outside your control, both the relevant prophecies about what just what Event that Hero is supposed to be about, and what is vaguely implied to be the game designers and the player.
The Nephalem (those who have awakened humanity's original power as angel/demon hybrids) in Diablo III are not mentioned in the Scroll of Fate and thus are the only ones capable of averting anything that is written in it.

Web Comics

In Sluggy Freelance Oasis is said to be one of small number of beings who aren't part of the Web of Fate and has the potential to severely screw up destiny, possibly leading to The End of the World as We Know It.
In Digger, wombats are rarely, if ever, mentioned in any prophecy even when things they cause are (such as the hole Digger uses to reach the surface at the story's beginning). This is actually Justified, as one of Digger's ancestors demanded making his children and descendants Immune to Fate his price for helping in the binding of a mad god. The only ones who seem able to give wombat-specific prophecies are slugs.
In Captain SNES, the Sovereign of Sorrow is capable of seeing everyone's future... except Schrodinger the cat. This character has already interfered with several of the Sovereign's prophecies.
K from Blip is a "cosmic mistake"—God himself somehow never foresaw her existence, so he had no place for her in his predestined plan. Any action of hers has the potential to completely upend God's plans. (K herself is completely unaware of any of this.) This doesn't, however, mean she's immune from being a Cosmic Plaything.
According to characters in Homestuck, Equius has this power. However, he's very traditional and predictable to those who know him, rendering it dubiously useful. It isn't revealed until after he's dead either.
Parson from Erfworld, by virtue of being able to subvert and outright break some of the rules that define Erfworld. Some residents of Erfworld hope that he will be able to break the "game" and bring true peace. Others are terrified of him for the same reason.

Web Original

In Thalia's Musings, the Fates wonder if Thalia and thus the rest of the Muses are this. The Fates don't like this idea.