A person characterized by two things — she gives correct and accurate warnings and predictions, and what she says is consistently mocked or ignored by the rest of the cast. You would think that the other characters would eventually decide that she can be trusted, but they seldom do. A particularly cruel plot twist is for the rest of the cast to believe Cassandra on the one and only time she is wrong, just to maintain the status quo. Cassandra usually has some sort of personality quirk that makes her seem less believable, or her information may come from epistemologically shaky grounds like Tarot cards or dreams, but her record of near-perfect accuracy really should be enough to make the others listen to her.
The Trope Namer is the mythical seer Cassandra, who was cursed by the god Apollo to give prophecies which were always true but never believed, thus making this trope Older Than Feudalism.
In natural disaster movies or Science Is Bad stories, Cassandra will usually be an Ignored Expert: a scientist or other expert acting as the lone voice of sanity. This character's role is to warn the others not to take a particular course of action — that will, of course, be taken. On the other hand, if Cassandra is one of the underclass, such as a street preacher or one of those Crazy Homeless People, the Doomsayer trope applies.
Subtrope of Cassandra Truth. Compare Crying Wolf, where a character is not believed when he tells the truth because everything else he's said has been a lie, and Dude, Where's My Respect?, which is often the result of this. See also Harbinger of Impending Doom. Cassandra Did It is when the cast add insult to injury by blaming Cassandra for the very disaster she tried to warn them about.
If Cassandra is a Waif Prophet or an Oracular Urchin, this may be because of All the Other Reindeer.
Idiot Hero Daiya of Gaiking: Legend of Daiku Maryu tells stories of monsters that attacked him and his father five years ago, and that his father is still alive somewhere, but nobody believes him. In the first episode, however, Kaiju turn up and begin attacking.
Subverted in Judge Dredd with Psi Judge Cassandra Anderson. As Mega-City One's most powerful psychic, her predictions are generally taken very seriously by everyone.
In A Reckless Frame of Mind Harry was the victim of a Cassandra Curse which meant that whatever he said, wrote or gestured was both the absolute truth and interpreted as a deliberate lie.
In Space Jam the basketball players, whose talent was stolen by the tiny aliens ask a cliché fortune teller, who actually finds out their problem (Talent stolen by tiny little aliens to play a basketball game against Bugs Bunny), but because it sounds too weird, they don't believe her.
The Good Son uses a variant on this when the child psychologist believes the wrong child to be telling the truth.
In Tower Of Terror, no one believed Abigail when she claimed that Sally Shine's nanny used magic to curse the hotel. As it turns out, she was lying anyway, making this a subversion.
The protagonist of Werner Herzog's Heart of Glass, the clairvoyant cowherd Hias. Although his (non-stop) prophecies come invariably true, most of the townsfolk treat him as a weirdo.
Pain and Gain: Ed Du Bois is the only human being who catches on the fact the main trio are vicious criminals. Nobody takes him seriously.
Sarah Connor in Terminator 2.
Live Action TV
In pretty much every haunted place investigation, one or both parents always discount "imaginary" friends their child has made (even if said child never has before), or strange behavior from the family pet, even with a slew of other unusual goings on such as loud noises, temperature drops and the likes, combined with other compelling evidence.
Dr.House is pretty much always right, he even says so, and yet, the other doctors continue to contradict him in every which way.
Subverted because he's also consistently wrong for most of each episode, and occasionally (though rarely) wrong all the way through. He's almost always eventually right, not always right. The reason he has the other doctors around is to prove him wrong until he's right.
They hang a lampshade on this in one episode, where House has to diagnose an epidemic on a plane without his usual medical team. He recruits a few passengers to help his thought process, giving instructions like "Contradict everything I say."
In Firefly, River freaks out = something bad happens is common, and yet Simon still always tries to convince her that there is nothing to worry about. Finally subverted in the movie, where they use her ability to sense trouble as an early warning system.
In Mal and company's defense, she is crazy. Remember the fear of Book's hair?
And if Zoe didn't have things to do, she'd be hiding with River.
Buffy was in this situation a few times, such as when she thinks her mother's new boyfriend is evil and that her new college roommate is a demon. In both of these instances, the others assume her to be overreacting to feeling uncomfortable about having her mother dating someone (who actually seems very nice) and having a roommate who's just very annoying.
Monk, while generally given some degree of respect, is often not believed despite being right almost every time.
The people who know him have learned to believe him, even when his theories sound crazy.
Stottlemeyer: Is he sure?
Disher:(beat) He's Monk!
Though he's pretty much guaranteed to be disbelieved if he suspects a murder while on vacation.
In the pilot episode of Buck Rogers in the 25th Century, Buck himself is seen as The Cassandra by Earth. He was awakened on Princess Ardala's ship and returned to Earth. He saw fresh laser burns on his ship, and concludes Ardala's ship has weapons on board, contrary to what the Princess insists.
Psych has Shawn, who acts psychic to give the police a reason, however flimsy, to listen to him. Now they often request his help, but they continue to display disbelief. Shawn's antics seem to simultaneously raise and lower his credibility.
There was a Dead Ringers sketch which parodied this by having TV characters known for this given a new boss who enthusiastically praised their track record and agreed with what they had to say.
Doctor Who: The Doctor. How many times has he charged around trying to get people to believe what he's saying? That he's talking about alien invasions and often dresses like a complete weirdo probably doesn't help his case. And unlike many other people on this list, he's usually not dealing with the same basic cast every episode.
Subverted in the new series: UNIT trusts the Doctor, just not enough to listen to his advice about running away from the Sontarans. Also, using a metaphor involving the sonic screwdriver and a pane of glass, he managed to convince Yvonne Hartman, leader of Torchwood 1, that the dimensional device was tearing holes in reality and she had to stop. That didn't prevent the Cybermen and the Daleks from invading, though.
And in the episode "Midnight", it becomes apparent that without a companion around, his social skills might not be sufficient to get people to believe him - resulting in total Nightmare Fuel.
On one occasion, while within the biggest library in the universe, he convinced a group of aliens to "look him up". They do. And behave themselves afterwards.
Recent seasons have many people believe that The Doctor is technically right, but there wouldn't be trouble in the first place if he'd just stay the hell away.
Except after seeing "Turn Left" it turns out every bad thing he prevented would have happened anyway even if he'd died in the first episode of the season. the only reason the earth wasn't destroyed entirely was because of the secondary characters picking up a bit of the slack (not enough, but some).
Averted in "The Eleventh Hour". He warns the Atraxi against messing with Earth and tells them to run. They do. Really really fast.
Dangerous Davies, The Last Detective, is always right when he suspects there's more to a death than meets the eye. This does not stop his DI from belittling and ignoring him whenever possible.
Mulder gets a fair amount of this on The X-Files. Of course, this can be expected when you go around spewing epileptic trees. Sometimes, he may get the details wrong, but the overall theory will be right. Other times, he uses a shotgun effect and throws out a bunch of different theories, but one of them is right. Subverted at the times The Conspiracy takes steps to have him ignored.
G'Kar of Babylon 5 has been described as JMS's Cassandra: at various points, he predicts what will happen; but no one believes him, mostly because they don't want to. For example, he tries to warn other races that the Centauri, having conquered the Narn, will turn their attention to others... which they promptly do. And other times, people who know he's telling the truth ahemDelenn and Sinclairahem won't back him up because they don't want the information getting out yet.
In an episode of Columbo, some corrupt local politician pulled strings to have Columbo assigned to investigate the crime he committed, thinking Columbo was too "bumbling and stupid" to catch him... even though Columbo had successfully solved every single case he'd ever been assigned to solve (or at least all the ones seen by the audience). This was especially common with early-season Columbo.
Alison DuBois of Medium gets this from her own husband almost Once an Episode. (Interestingly, the district attorney and his lot are much more open to believing her - they only refuse to act because it would bring suspicion on them, not because they discount her abilities). She has a dream and wakes up freaked out next to him; Joe tells her to go back to sleep because it was "just a dream". This despite the fact that every week she has a prophetic dream, and the entire plot revolves around how she prevents, corrects, or figures out what her dream meant.
One episode of Red Dwarf's eighth season introduced Cassandra, the AI who could see the future including her fate — accidentally being destroyed by Dave Lister, despite his best efforts. They weren't even trying to be subtle there.
In Veronica Mars, Veronica will, without fail, get to the bottom of any mystery, embarrassing the guilty Jerk Jock, Alpha Bitch, or idiot sheriff in the process. Despite this, the town residents only ever react to her questioning them with smug indifference. Not only that, but she spends the entire first season trying to figure out who killed her best friend, Lilly. It turns out to have been Aaron Echolls, the father of Lilly's ex-boyfriend and Veronica's boyfriend at the time she figures it out. Unfortunately, when it goes to trial he gets off Scott free (not counting getting shot in the head by Wiedmann) because Logan destroys the sex tapes, and no one believes Veronica or Logan when they testify that they saw the tapes themselves. Even worse, Aaron nearly burned Veronica to death and beat the crap out of her father, but in the trial he claims that Veronica accidentally crashed her car, and they were waiting at the nearest house when Keith found them and attacked him. And the only other witness, the owner of the house, mysteriously went missing. Seriously though, you think these people would learn to trust V's gut once in a while.
Rumzan the punkah wallah in It Ain't Half Hot Mum. Much of what he observes early on is often borne out by the end of an episode, but no-one pays any attention, presumably for racial reasons.
LOST's Sayid Jarrah has remarkably correct intuition in the early seasons...but more often than not it's ignored by Jack, etc. See Three Minutes, where Sayid deduces that Michael is working with the Others, but can't stop Jack, Kate, Hurley and Sawyer from following him right into a trap.
Throughout the first season of Merlin Morgana was seldom believed when she had a prophetic nightmare about something. Justified in that she was afraid to reveal her powers and so passed off her visions as vague "feelings about things" and subverted in that the people who did believe her wanted to keep her in the dark about how accurate her dreams really were.
In Homeland, Carrie Matheson is right about everything, always. No one believes her, ever, not even Saul, her friend and mentor. Of course, given that she is bipolar....
Amusingly this series is also a direct retelling of the myth with Brody in the role of Apollo.
In Survivor, the aptly-named Sandra Diaz-Twine played this role in both of her seasons. In Pearl Islands, she didn't buy Jonny Fairplay's "dead grandma" lie for a second but everyone else believed it. It went even further in Heroes vs. Villains where she tried multiple times to tell the Heroes that Russell was untrustworthy and that they needed to vote him out but they just wouldn't listen to her.
On The Mentalist, Patrick Jane is never wrong. About anything. Ever. If he expresses an opinion about how a crime was done, where it was done, who did it, or what a suspect is thinking or feeling, he's always right on the money. Doesn't stop Lisbon and the CBI brass from regularly assuming that he just happens to be wrong this time, his previous 100% success rate notwithstanding.
Star Trek: The Next Generation of course has Wesley Crusher, who's never believed because of his youth, or presumed inexperience. Not only is he consistently right, but several times his ideas could be trivially verified, but are ignored.
And Star Trek: Voyager has Reginald Barclay who's ignored because of his stammer and general oddness.
The title character on Eli Stone is an almost literal Cassandra: he constantly (and accurately) predicts disaster with his visions, and every time he has such a vision he has to convince everyone around him that he's not crazy all over again.
In "Goddess of Yesterday" but Caroline B. Cooney, a novel set in Troy, Cassandra herself exploits her curse in a moment of Genre Savvy as the main character is trying to escape the city by calling out that someone is trying to leave through the gate. The main character panics for a moment until she realizes that because no one believes Cassandra no one is bothering to look at her, giving her a chance to escape, and Cassandra blows her a kiss from her tower.
No one listens to Mikhail Kutuzov in War and Peace. Battle of Austerlitz? Bad idea, says Kutuzov. The Russians intervene and get their asses handed to them and Napoleon conquers Austria. Oh well, no big deal.
Several of the earlier Sherlock Holmes stories, perhaps most particularly A Study in Scarlet, show the great detective being mocked by the official police for his unusual methods and seemingly bizarre theories. Over time, however, as they find he's right almost unfailingly, the police shift their opinion and become admirers of Holmes. Lestrade even comments on it in The Adventure of the Six Napoleons, saying that they're not at all jealous of him at Scotland Yard, but on the contrary, "we are very proud of you."
Harry himself, despite being The Chosen One, frequently gets this treatment, especially from his best friends. So much so that Dumbledore freely admits that part of his plan in the seventh book is counting on Hermione's Arbitrary Skepticism to slow Harry down long enough to think things through properly.
Professor Trelawny is a reverse Cassandra, as the only time she dismisses one of her predictions is when it's correct. A more subtle one occurs in Half-Blood Prince. Harry is hiding from Trelawny, who's wandering drunkenly through the school, and pulling cards from a deck. Though it's never stated, it's entirely possible she's doing a reading on Harry. One of the cards she interprets as meaning the subject dislikes her (Harry can't stand Trelawny). She thinks about it for a second, and says "that can't be right," and starts going through the cards again. She also plays the trope straight on several occasions. When she does make an accurate prediction, her reputation means that nobody takes it seriously. This includes Harry shrugging off the prophecy about Pettigrew escaping and her statement that the first to "rise from" the staff table will die first which is true on both counts for Dumbledore.
Antryg Windrose, the title character of The Windrose Chronicles, uses Holmes-ish deductive reasoning to figure out things that everyone else then assumes only the villain could know. Between that and his checkered past, he's never believed by anyone in a position of authority - and on the rare occasions when this is not true, he winds up being banned, banished and locked up anyway for telling truths people don't want to hear. Fortunately, he has the patience of a saint.
Astrid in Garry Kilworth's novel House of Tribes is known far and wide for her prophetic powers. Naturally, when one of her visions is politically inconvenient, everyone comes up with reasons to assume she's wrong and blunders ahead anyway. After her vision comes true, her prophetic stock shoots up twenty places...until the next vision, which is again inconvenient and is again ignored by quite a lot of characters. There's a message in there somewhere.
Heralds of Valdemar: In Arrow's Fall, Empath Talia has demonstrated a flawless track record of reading people, but is still doubted and ridiculed when she attempts to expose Evil Chancellor Lord Orthallen. Her fellow Heralds are at least willing to give her the benefit of the doubt, but Valdemar's councilors are not Heralds and see no reason to believe a girl barely out of training over a man with 20 years of service to the kingdom and enormous personal and political power. Orthallen, in his turn, recognizes Talia's threat to him and sows rumors to cast doubt on her reliability.
Mairi Urqhuart in Janet Lunn's novel Shadow In Hawthorn Bay. Mairi has second sight and is able to predict the future, but the other people in her Upper Canada settlement do not not believe this. When she tries to tell people about her predictions, the usual response is to ignore her, say she's crazy, or tell her to stop frightening people with her gloomy predictions. When her predictions come true, she is accused of using witchcraft to make them come true.
In Everworld, the heroes meet Cassandra. Being Genre Savvy, they tell themselves that they have to believe her, but we see them suddenly develop a five-second amnesia, so they don't remember what she said, only that it was BS.
Christopher Durang's Vanya and Sonya and Masha and Spike combines this with Sassy Black Woman. Cassandra, the housekeeper, continually makes prophesies that range from, "beware Greeks bearing gifts," to "avoid real estate transactions for the next 15 years," that are always ignored. Later subverted when she gets tired of her prophesies being ignored and decides to change the future using Voodoo.
Feizhi from Golden Sun makes many accurate predictions, but her father dismisses them as coincidences. If the player helps her save her friend Hsu, her father finally admits she can tell the future.
Commander Shepard from Mass Effect is one as far as the brass is concerned. S/he can't convince them of anything important, no matter how damning the evidence presented is.
Most of Shepard's predictions sound absurdly crazy from the perspective of the council or anyone else. The Reapers went to a lot of trouble to make sure there was virtually no evidence of their existence. The council very quickly changes their mind about Saren being involved in Eden Prime when s/he presented hard evidence. Admittedly, the witness testimony should have been given more weight considering he was identified by name by another Spectre.
Gets even more absurd in Mass Effect 2, where the council (if you kept them alive) STILL doesn't believe you. Despite you having saved them personally from a Reaper. They blame it on the Geth, even if Legion (a geth) is in your party and says "Nope, wasn't us."
Shepard: So the geth believed your proof that the Reapers were coming back?
Legion: Of course.
Shepard: ...That must have been nice.
Daelin Proudmoore from Warcraft. After fighting a war with the (Old) genocidal Horde, he begins to attack their new settlements on Kalimdor after their demonic curse is lifted, claiming that the Horde will never change despite the protest of his daughter Jaina. Come Mists of Pandaria and the New Horde led by Garrosh Hellscream has attempted to take over Kalimdor, destroyed the formally semi-neutral city of his daughter and is now waging a war to control all of Azeroth. In her grief Jaina admits that her father was right all along in front of his statue after the destruction of Theramore.
There is a gypsy moth in the Chip 'n Dale Rescue Rangers episode who predicts a soon and certain end to Chip's life. The Rangers' leader refuses to believe in that prophecy and continues on the case until all details but one have come true. The name of the moth is... Cassandra.
Candace is constantly trying to prove to her mother that her brothers, the title characters, build all kinds of crazy projects in their backyard, but the evidence of said crazy projects has always vanished by the time she gets her mother's attention.
Vanessa tries to prove to her mother her father is a Mad Scientist, but it always fails, largely because Doctor Doofenshmirtz isn't really good at villainy.
Travis the head louse in the "Lice Capades" episode of South Park.
This is Toxic Crusaders character Psycho in a nutshell: his entire purpose is to point out to Dr. Killemoff how his latest plan can go wrong, usually involving really unlikely circumstances that nevertheless always end up happening and yet Killemoff never listens to him, despite his predictions having always been right.
Cassandra herself was a secondary character in the TV series based on Disney's Hercules. She's very bitter about her lot in life.
Coop of Kid vs. Kat constantly tries to warn his town about Kat's evil schemes, only to earn a reputation as both a liar and a lunatic. However, unlike most examples, Coop gradually seems to realize his status as The Cassandra, eventually focusing on simply sabotaging Kat's plans privately instead of warning people about them. Fortunately, he's thrown a bone in the form of his best friend Dennis and his girlfriend Fiona, who are both aware of Kat's actual identity and are happy to help Coop out.
PJ on Goof Troop is almost always the first (if not the only) person to notice something's gone wrong. He's also usually ignored, due to his total lack of assertiveness. However, "Tub Be or Not Tub Be" and "Talent to the Max" are even worse—he, who doesn't lie for his own self-interest without coaxing, and who has Undying Loyalty towards Max, is accused of betraying him. He tries to tell Max that he didn't mean to cheat and was trying to undo all the booby traps in the former, and that Max needs to dump the magic hat like a bad habit in the latter, but Max doesn't believe him.
The Novikov Self-Consistency Principle is a conjecture on Time Travel, which is theoretically possible under some interpretations of general relativity theory. Basically, if any event caused by a time traveler could change the timeline, then the probability of that event happening is zero. Time paradoxes are impossible no matter how much screaming you do.
Many of the early whistleblowers in The Thirties had this problem. The ruling bodies of Europe were not able to grasp the dangers of fascism until war was almost upon them. Thus, the intellectuals who tried to warn about immanent danger were often ridiculed.