(Just after Prophet states that destroying the facility could lead to the aliens' return) But everyone blows him off, and sure enough, the aliens come back. Wow, who could have seen that coming? If only there were someone around here whose name means "someone who predicts things"!
Subverted by Dr. Kabuto from Mazinger Z. Despite he was a renowned scientist and a witness, he did not try to warn the world of what had happened in Bardos Island (to wit: one of his colleagues had murdered the entire archaeological expedition minus Kabuto after finding an army of ancient Humongous Mecha buried in the underground mazes of the island) and what Dr.Hell was planning (to wit: Take Over the World), opting for shutting himself away to build his super-weapon. Of course, he could have reasonably thought that nobody would believe his story.(Would you?)
Chief Engineer Precia Testarossa in Magical Girl Lyrical NanohaThe Movie First. Even though she told the corporate executives of her company that the reactor she was developing was a new design and had a chance of a meltdown, they slashed the testing time of the reactor from one month down to ten days. They also had the safety protocols of the reactor done by their own people, who were more interested in getting the testing done quickly rather than properly. Needless to say, the Chief Engineer's fears were realized on the day of the reactor's live test run, and a meltdown occurred that killed several civilians in the process, including her daughter, Alicia.
Vividred Operation: Despite Kenjirou's knowledge of the threat that the Alone had presented to humanity, the scientific community remained skeptical and excommunicated him.
Superman's father, Jor-El, was at one point the Trope Namer, having correctly predicted the destruction of Krypton, but his warnings were not heeded, as demonstrated in the page image.
One issue of the Nineties JLA features a city of sentient bacteria living in the folds of a young boys' brain. The bacteria mine the brain tissue to harness neural electricity for energy which is slowly killing him. One scientist is aware that "the world" is alive and they are killing it, but no-one will listen. Eventually doctors are forced to cut out the city with a laser, killing them all, but before it does the scientist and his wife load their son into a vessel and lauch it towards the liver, where "the iron-rich blood will give him powers and abilities undreamt of by our race". The last panel of the comic is the rocket lying on the surface of the liver, with two bacteria moving towards it.
This is also the backstory of Superman villain Brainiac as of the New 52; he was the greatest scientist of Yod-Colu, but his discovery of an impending threat to the planet was laughed at. He was even labeled insane and sent into exile. It wasn't long before he returned, used his technologies to compile a record of the planet's culture and history, and killed most of the population.
Parodied in normalman, where Norm's father was a no-name accountant who irrationally came to the conclusion that his planet was doomed, bought a rocket at a convenience store, and sent his son into space. Norm's mother killed him immediately after he did so.
Subverted in a short strip written by Alan Moore for 2000 AD. A great man named R-Thur is rejected by the planet Klakton's other top scientists after making apocalyptic predictions, he plans to send his infant son N-Ree to a faraway planet called "Earth" where, because of the planet's lower gravity, N-Ree would "be able to fly, see through walls, and bounce bullets off his chest". After he sends N-Ree away in an escape rocket, R-Thur assures his wife that they will never see their son again, and begin to prepare for their eventual demise. It's gonna happen... It's gonna happen... aaaaand...
R-Thur: Er... L-Sie, I don't quite know how to tell you this but, ...er... I think I might have been wrong about Klakton exploding, heh heh! L-Sie:#*@^#! R-Thur: Gosh, L-Sie, anybody can make a mistake!
The same parody of Jor-El is the origin of Mr Might, Awkwardman's father in DC Comics' Self-Parody book Inferior Five. Mr Might was Barb-Ell the son of Dumb-Ell of the planet Neon. He was sent to Earth as an infant because he was convinced Neon was about to explode. As with R-Thur and normalman's father, he was completely wrong.
Parodied as well with Brum-El, of Ambush Bug. However, Brum-El was not a scientist, just The Dandy in a very advanced civilization, and instead of saving his family, he chose to save his wardrobe. Again, when his planet failed to be destroyed, he was just mocked and left naked.
Transformers: Stormbringer: The Decepticon scientist Thunderwing was concerned that the war was damaging Cybertron's environment to the extent the planet would eventually be rendered uninhabitable, and tried to reach out to every scientist he knew (and Swerve) to try and solve the problem. They rejected his claims on the grounds that he didn't have enough evidence. So he created a means by which Cybertronians would be able to survive the on-coming cataclysm, and tested it on himself. The result? An unstoppable insane behemoth that required the combined firepower of both armies to just slow down, and the utter annihilation of a large chunk of Cybertron. Whoops.
One chapter of Eugenesis opens with a statement delivered to Optimus Prime from the First Church of Primus some time after Unicron's defeat in 1991 explaining that he was going to return some time around 2005 or 2006. According to the backstory, they were ignored. And then in 2006 Unicron returned and attacked Cybertron. (Optimus gets excused because he was dead.)
Films — Animation
In Final Fantasy: The Spirits Within Dr. Sid's claims that the Phantoms are actually Exactly What It Says on the Tin are met with this trope. This is all the more unreasonable when one reflects that Dr. Sid is the inventor of not only the only weapons that have had any effect at all upon the Phantoms, but is also the inventor of the energy shields that keep Earth's remaining cities intact.
In Fantastic Mr. Fox, Fox chooses to ignore his real estate agent's advice not to move into Boggis, Bunce and Bean territory. However it wasn't because he lived there that they hated him, it was because he stole from them.
Films — Live-Action
In Man of Steel, a variation occurs on the Superman myth pertaining to Jor-El. Krypton's destruction was the Kryptonians' own doing as they attempted to tap the planet core for power when all other sources were exhausted. Jor-El warned that it was a colossally stupid idea, and was disregarded, and he warned again that the planet's doom could be mere weeks away some time after it was implemented, and only General Zod believed him.
Dr. Dalton in Dantes Peak, although the movie does subvert how the trope is usually played — Dr. Dalton doesn't have enough conclusive evidence, and the economy of the town could be ruined if he was wrong. The second Dr. Dalton finds concrete proof, it's immediately taken seriously; the town was in the middle of a town meeting discussing the evacuation plan when the volcano started erupting.
Adrian Helmsley (Chiwetel Ejiofor) in 2012 is a subversion. He brings a written report of his findings about the imminent end of the world directly to White House Chief of Staff Anheuser. Anheuser initially dismisses him, until Helmsley insists; Anheuser takes one look at the report and immediately brings it to the President's attention.
Anne Heche in Volcano, which at some points seems to be set in an alternate reality where the very existence of volcanoes is an obscure geological fact completely unfamiliar to the public. Although that's probably less "people don't know what a volcano is" and more "no-one expects a volcano to erupt in the middle of Los Angeles."
TV Anchorwoman: Well, we now have a name for this crisis. It is, according to the US Geological Survey, a "volcano"...
A rare non-scientist example, Carter Blake in Deep Blue Sea is a "shark wrangler" who correctly points out that using genetic engineering to make sharks (already apex predators) smarter is not a good idea. He's blackmailed by the Hot Scientist into keeping quiet, but at least he tried to warn her of the danger.
Jack Hall and his son, Sam, in The Day After Tomorrow. First the Vice President ignores Jack's warnings about climate change. And then an entire public library full of survivors ignores Sam's warnings about the temperature even after he tells them he knows this because his father is a government climatologist.
This happens in tons of horror movies — for example, Jaws (as referenced below).
David Duchovny's Ira Kane in Evolution and the associated napalming. This has less to do with the government distrusting Kane (which they do thanks to his huge screw-up with the anthrax vaccine) and more with him being a complete Jerk Ass to his former commanding officer, who's in charge of the napalming.
Flash Gordon. NASA scientist Hans Zarkov warned that the unusual events were the result of an an attack on the Earth. He was fired from NASA and the authorities rejected his ideas as "irrational". It turned out that he was absolutely correct: the phenomena were sent by the Emperor Ming to amuse himself.
In Day of the Wolves, Chief of Police Pete Anderson tries to warn the town council that Wellerton is vulnerable to a criminal takeover. They fire him.
In City of Ember, Doon is the only one convinced that the eponymous city's generator is beyond repair, and it needs to be overhauled, or the city abandoned. Naturally, the older generation tells him to shut up. It turns out he and his Love Interest are Legacy Characters (of sorts) to their fathers, who were part of a cabal who foresaw the collapse years ago. Her father died trying to find a solution. (This really only happens in the movie, not in the book.)
If you're ever in a lab trying to free animals and a scientist who works there begs you not to because "they're infected and it only takes one bite", don't do what the activists of 28 Days Later did and completely ignore him.
In A.E. van Vogt's The Voyage of the Space Beagle, the lone nexialist (a scientist whose specialty is nonspecialization) is surrounded by an expedition that laughs him off in spite of his increasingly frequent responsibility for saving the entire ship. This eventually escalates to the point where he hypnotizes the entire crew and enslaves them for three years in a massive effort to defeat an insatiable nebula-like monster that has nearly sterilized its galaxy.
The Gods Themselves a science fiction novel by Isaac Asimov has three Jor-Els attempting to warn everyone of a danger. One is an alien trying to warn her planet and the two others are human trying to warn Earth. The name of the novel (as well as those of the three parts) comes from the quote, "Against stupidity the gods themselves contend in vain."
Subverted in Invisible Man: the main character realizes that there's going to be a riot, but his warnings come to nothing because those he's warning want there to be a riot so they can gain power from the resulting chaos.
Superman: Naturally, Jor-El himself in the surprisingly good Adaptation Expansion novel The Last Days of Krypton. For one point in defense of his detractors, Jor-El had already predicted the end of Krypton in a fair number of ways already by the end of the book.
Happens big time in the short story Nightfall by Isaac Asimov (later adapted into a full novel by him and Robert Silverman). Scientists from many different fields discover that soon, darkness will fall over the planet Kalgash for one night (it happens every 2048 years; the planet is surrounded by 6 suns so it has constant light). Astronomers predict the actual event, archaeologists predict the mass destruction (it's happened previously), psychologists predict the human reaction to it, and no one believes them. They're reviled, denounced, and eventually, 100% correct.
Hari Seldon in Asimov's Foundation Series, even though he did have some listen to him. Partly because the collapse is happening so slowly that people don't really notice beyond occasional "this used to work better in my day". Seldon himself didn't believe it in the prequels until Chetter Hummin showed it to him. In fact, Hummin had Seldon develop psychohistory precisely to find a solution for the problem.
In Nevil Shute's No Highway, Theodore Honey, a scientist with the Royal Aircraft Establishment is flying to investigate a plane crash. He's told the authorities that he thinks the crashes are due to metal fatigue and to ground all planes that are getting on a bit. To his horror he realises that the plane he's in should have been grounded because it's flown far too many miles and he runs around telling everyone what to do if the wings fall off. No one believes him, so he lifts the undercarriage while the plane's on the ground.
In Going Postal, Clacks engineer Mr. Pony keeps insisting that the Grand Trunk's semaphore towers need to undergo proper maintenance or the whole business will go under. Unfortunately, his superiors are only concerned with immediate profits, and think that shutting down the towers for an extended period of time is madness, since it will lose money (plus, there's the matter of them buying the Trunk on embezzled funds). When he presents hard facts and explains the exact minimum amount of money he'd need to at least keep the service running a while longer, his boss (Big Bad Reacher Gilt) agrees to give him a quarter of it, and makes a grand show of it as though he's being generous. Of course, in this case Giltdoes in fact believe the engineer, but just doesn't care, because he knows that even if the Clacks did collapse, he would still be able to make a massive profit selling the business to someone else, regardless of whether it was a total shambles.
In the Harry Turtledove novel Supervolcano: Eruption, one of the main characters is a geologist studying Yellowstone park. Despite being a clear expert (and even being interviewed on television news as a geology expert several times), and despite a lot of pretty strong scientific evidence that something was going on, she can't get anyone to take her warnings about imminent eruption of a supervolcano under Yellowstone park. The justification the Government gave her was basically that an eruption on that scale would be too big a disaster for the government to respond to anyway, so there was no point in worrying about it.
In Jurassic Park, Hammond invites a group of various experts to his park before it opens to advise him, and basically all of them become this. Most vocal are Malcolm, who insists that trying to replicate an ecosystem that disappeared millions of years ago is a fool's errand, and Muldoon, who says that the Velociraptors are too intelligent to be held and must be killed before they escape. Both turn out to be right.
Honor Harrington: Assorted military analysts in the Solarian League try desperately to inform their superiors, political and military, that the League fleets are completely and hilariously outclassed by the fleets fielded by the navies involved in the Haven-Manticoran War. They find out to their horror that they underestimated the technology gap.
A Song of Ice and Fire: The Night's Watch have plenty of proof that the Others are coming and mean to cross the Wall. Good luck trying to get King's Landing to listen, even after repeated attempts... Only Stannis takes them seriously.
ALF's grandma. She was the only one who'd guess that Melmac could explode, and could save the planet... Though they locked her in a nuthouse.
Doctor Who: The Doctor finds himself in this situation quite often, what with being both highly intelligent and highly eccentric.
Still, it's subverted in the new series episode "Army of Ghosts", where he tells the head of Torchwood Institute to stop punching holes in reality. She brushes him off as being too alien-supremacist... then, when the Doctor sits back to watch, relents and admits that she should listen to the guy who, not only is named in her organization's charter, but has a very long pedigree that she's very well aware of about being right on these matters..
An earlier subversion occurs, along with a Lampshade Hanging, in "Four to Doomsday" in a fleeting moment of Genre Savvyness. Referring to an impending alien invasion:
Tegan: We've got to get to Earth and warn them! The Doctor: Of what? Who'll believe us? We'll be laughed at.
In between those two subversions, there's an example of it played straight in "Dalek". The Ninth Doctor tries to warn everybody of just how dangerous the Dalek is, but nobody believes him until all of the soldiers and most of the scientists in the silo have been killed by it.
Kim Delaney's character in the miniseries Ten Point Five fits into this. Of course, the Cassandra Truth reception her warnings received wasn't helped by her abrasive personality.
Adama in the original Battlestar Galactica warns everyone that the Cylons are up to no good. No one believes him.
Carl Kolchak in the original film and series (The Night Stalker, The Night Strangler (films) and Kolchak: The Night Stalker (series)) is almost always entirely alone in noticing what is really happening.
The Invaders. David Vincent spends the entire series struggling in vain to warn people of the alien invasion taking place in the series. It doesn't help that the evidence has a nasty habit of disappearing right in front of his eyes and the people he goes to for help have a nasty tendency to be alien agents.
The final season of Lexx has Dr. Ernst Longbore, a Genius Cripple who used to belong to a group of scientists working on a particle accelerator capable of determining the mass of the Higgs boson particle. He became an Ignored Expert after realizing that determining the particle's mass would trigger a massive chain reaction that would implode the planet into a dense chunk of matter the size of a pea (apparently, this is the fate of every civilization that tries to determine the Higgs boson's mass). Having lost his career and academic standing, he's spent his remaining time with a small cult of college-aged followers working on a way to escape Earth.
In the second season of Heroes, Mohinder opens the very first episode warning people about the virus that killed his sister. Nobody listens, and to add insult to injury, the people who do end up destroying the virus find out about it from totally unrelated sources.
In the episode "The Inner Light", an alien probe connects to the mind of Capt. Picard, who seems to find himself living on a pre-space-flight planet; he spends years there, trying to figure out where he is by studying the stars and the movement of the sun. Eventually, he builds a life for himself, starts a family, and even learns to play the flute. Unfortunately, he uncovers from his study of the sun that the drought they have been enduring is the result of the sun getting ready to go nova very soon. His efforts to warn the people of his community and the government of the planet at first seem to go ignored, and it looks like this trope is going to be in effect. But they reveal they already knew about the problem but were powerless to do anything about it. The truth is they were just trying to prevent a panic while working on a secret project to preserve something of their civilization: a special probe that would be launched into space using their most advanced rocketry, in hopes of finding someone in the future to carry on the memory of their people
In "Q Who", the ship is sent 7,000 light years by Q, placing them unknowingly in an area where the Borg are active. Picard chooses to ignore Guinan's advice to turn back now. (Though when they actually encounter the Borg, and Guinan tells them to protect themselves, they finally take her advice.)
SF Debris sees Worf as this, as he frequently gives sound advice about how best to deal with enemies and crises, but never allowed to act until it's powerful enough to beat him, causing The Worf Effect.
Though in fairness, Clarkson had a terrible resume on the show before this, almost killing a man with a false diagnosis, and then missing the obvious signs that a patient was suicidal.
In the Masters Of Horror episode "The Screwfly Solution", Alan and Barney have a meeting in Washington D.C. with members of the government and the military. They explain that the ongoing Gendercide is a concerted attempt to exterminate the human race, that the women in the infected areas need to be evacuated, and that the men, especially those in important positions, need to take medication that will lead to chemical castration to prevent them from turning into murderers. All their advice is ignored.
Harry Chapin's The Rock tells this story straight.
The story of the ride Expedition Everest at Walt Disney World is that you're part of a team of mountaineers taking a train ride to Everest Base Camp that takes a shortcut along the slopes of a mountain rumored to be the home of the Yeti. Part of the queue area is a museum run by a local naturalist, Professor Pema Dorje, presenting his evidence that the Yeti is real and dangerous, including a plaque at the end warning people of the danger of entering its domain, below which is a note by the operators of the railroad saying they don't agree with or endorse his opinions. If you board the ride vehicle, you're "ignoring" this warning and going to the mountain anyway, and your train gets attacked by a Yeti, making Professor Dorje an example of this trope.
In Mass Effect, one of the few surviving scientists in the lower levels of the Peak 15 research station is dismissed as mad by every other person in the place (except for Shepard and company) for believing that the whole project for the recreation of the Rachni, who proceeded to go mad from isolating their queen from the rest of them, and devour just about everyone in the hot labs was a terrible mistake, and wanting to inform the rescue effort about it. "Crazy? I'm sane. God am I sane."
Manuel, a scientist encountered on Eden Prime. He's rambling and about to be sedated when Shepard encounters him, with his dialogue hinting that he may have looked into the Prothean Beacon himself and been driven insane as a result, something Liara later speculates could happen to those without the iron-will that Shepard and Saren have. As nonsensical as his hysterical babbling is without the context of the beacon's message, by the end of the game almost every single thing he says has turned out to be entirely correct.
In the first game, a scientist is working on scanning the Citadel's keepers to learn more about them. By the second game, he's discovered the basic truths about them and their connection to the Reapers, but no one will listen to him.
Shepard has conversed with a Reaper, and heard the final testimony of the Protheans, and yet, as soon as s/he's gone, the Alliance and the Council try to sweep it under the rug. The only ones who believe him/her are Anderson, Hackett and The Illusive Man. Made more ridiculous that the Asari are capable of mind melding, so really, the Asari councillor could simply read Shepard's mind to verify the truth about the Reapers and everything that Shepard has experienced. It's explained in the third game that it's because they are in denial.
In Superman: The Animated Series, Jor-El was actually discredited by Brainiac, who wanted to ensure his own survival over that of the Kryptonians.
Interestingly enough, the later series Legion Of Superheroes (not canonically related to the DCAU) subverted this, with a flashback revealing that Jor-El was believed, and enacted a plan to save Krypton using a new invention housed in the city of Kandor. But then Brainiac shrunk it, and...
Parodied by Dib in Invader Zim. He is perhaps the only person who believes Earth is in danger of alien invasion and is worried and he constantly speaks out about it and tries to expose Zim as an alien and a threat. Living in a Crapsack World means no one listens or cares, and he's continuously mocked and abused for his efforts to the point of Black Comedy. While his younger sister Gaz grudgingly admits Zim is an alien, she points out Zim is very lousy at trying to conquer it. Plus, his race has no real interest in conquering Earth; they just exiled him there and lied about it to Zim. However, some of Zim's plans did fail because of Dib's interference. Perhaps Dib simply needs to be calmer about it?
In a flashback episode of The Venture Bros. Hunter Gathers, and Brock Samson try to tell the rest of OSI that the Guild of Calamitous Intent is still around. No one believes them, ridiculing them for not fighting Sphinx. Sargent Hatred, The Mole for the Guild has Hunter relocated to Guam, and Brock relocated to "Rusty's blanket", a task for rookies. Given that in the present the Guild is a Weird Trade Union known to most super-scientists and wizards, something must have happened between then and now.
Done in Futurama episode "Jurassic Bark" one by one, the cast tries to jump into the lava to save the fossil. Each time, they are stopped and the Professor explains that they will die if they do. He finally reaches a peak of frustration and exclaims "Why is no one listening to me?? Professor! Lava! Hot!!"
Mighty Mouse: Ralph Bakshi, when he gave Mighty Mouse a Superman-like origin, created a Jor-El parody who tried (in vain) to warn other residents of the condemned building it'd be demolished.
Engineer Roger Boisjoly found evidence that an essential component of the Space Shuttle's rocket booster was rendered unreliable by cold temperaturesnote These being the O-rings, which create seals on the fuel tank; cold rendered the O-rings rigid and unpliable, meaning gaps in the seal were created; nobody listened to him, partly because the company that made the booster was in the middle of negotiating a new contract with NASA. A year after Bosjoly's discovery, the Challenger space shuttle exploded because of this particular design flaw.
It was actually a lot worse: the launch of Challenger went ahead that morning, despite the official receiving screaming memos ("Red Alert!" in red ink) not to launch. "Take off your engineering hat, and put on your management hat." Commissioner Richard Feynman discovered massive disconnect between management and engineers in the Space Shuttle program. Management routinely disregarded what engineers said.
Sir John Fastolf was the only English commander in France toward the end of the Hundred Years War who not only realized and was willing to declare publicly that England was, at long last, losing the war, but also had a constructive proposal for salvaging the situation. For his pains, he was disgraced after the defeat and turned into the clownish figure of Falstaff by Shakespeare. Shakespeare was originally going to call the character Oldcastle, but changed it to Falstaff at the insistence of his patron the Lord Chamberlain, descendant of the former. Ironically, the character himself is among Shakespeare's most beloved.
Unfortunately, this tends to be Truth in Television for scientists whose discoveries go against the established ideas of the time. One example is Dr. Alice Stewart, who showed a correlation between pre-natal X-ray screening and cancer, and was ignored for several years.
Ignaz Semmelweis discovered that childbed fever can be avoided by use of hand washing standards in clinics. His findings were rejected, and were only accepted after his death. The idea of disinfection only really took off after Robert Koch and Louis Pasteur produced definite proof of the relationship between germs and disease. Washing your hands to prevent infection was popular in England even before Semmelweis, but since the English scientists still believed in the theory of miasma, they were right for the wrong reasons. To be fair, Semmelweiss didn't advocate washing your hands with soap, he advocated washing them with carbolic acid (phenol, a known carcinogen), which doesn't exactly promote the kind of skin you'd see in a hand lotion commercial. You can see why folks might resist the idea. (Well, that, and Semmelweiss was by many accounts about as sane as Nikola Tesla.)
The Great New England Hurricane of 1938 was predicted to swerve out to sea by the National Weather Service, but instead kept moving due North and slammed into Long Island and the coast beyond. The lone Weather Service employee who had pointed out the threat of such a landfall was disregarded due to his lack of seniority, and no warnings were issued until after the storm had demolished regional communication lines. The predictions that it would veer out to sea were very reasonable and actually probably more likely to come true. The main problem was that nobody kept watch on it just in case it didn't change course as predicted.
Similar to the above, the death toll from the Hurricane that hit Galveston, Texas in 1900 would've probably been much less if the National Weather Service hadn't ignored information coming out of Cuba due to Pride.
An historical War & Politics example can be found in Sir Isaac Brock, the British General in charge of the defense of Upper Canada (present-day Ontario) against the United States in the War of 1812. He was one of a few who believed that war with the U.S. was imminent and one of fewer who actually cared about the implications this would have for British North America. He and a small number of other leaders (notably the Native Chief Tecumseh) took steps to prepare against a possible invasion (even his time collaborating with Tecumseh was only a short couple of days, and Brock's main focus was on making sure the militia would be ready). Although he died at Queenston Heights, his preparations (taken pretty much completely of his own accord) and his strategic skill in several battles ultimately secured the safety of Upper Canada. As his Wikipedia Article states:
"While many in Canada and Britain believed war could be averted, Brock began to ready the army and militia for what was to come. When the War of 1812 broke out, the populace was prepared, and quick victories at Fort Mackinac and Detroit crippled American invasion efforts. Brock's actions, particularly his success at Detroit, earned him a knighthood, membership in the Order of the Bath, accolades and the epithet "The Hero of Upper Canada"."
Harry Markopolos spent years trying to convince the SEC that a well-connected genius investor was running a massive Ponzi scheme. They all ignored him until Bernie Madoff's fund collapsed. Some have pointed out his abrasiveness made his message harder to swallow (he once called the SEC staff "a bunch of idiots"). Others have pointed out it was well deserved.
The Vajont Dam in Italy. When it was being constructed, three experts published studies warning that the nearby Mount Toc was in danger of collapsing into the artificial lake if the barrage's filling went ahead. They were ignored… and four years later, Mount Toc followed up on their predictions, earning Vajont the dubious honor of being the source of the largest man-made tsunami in history (a 250-meter-high, or 820-foot-high wall of water that wiped out several villages and killed thousands in its path).
Dutch engineer Johan van Veen. From 1937 on he started petitioning and warning the Dutch government to reinforce the diking system in the south-western part of the Netherlands. Nobody listened to him. Cue 1953, a freak storm and much of the province Zeeland was flooded, with 1800 people dead. After the stormflood... he got all of his plans approved and this started a 30 year project of protecting the south-western lands from the North Sea. Knowing the government would not listen to his warning, how did he sign his proposals before the fated storm? Dr. Cassandra.
Former Chair of the Commodity Futures Trading Commission Brooksley Born identified a problem that did not cause the financial crisis, but made the damage much worse. Naturally, she was ignored.
Senator Elizabeth Warren (D-MA), a longtime bankruptcy and contract lawyer and Harvard professor, started predicting the 2008 market crash in the 1980s. As the 2000s wore on, she continued to make hay about the issue, but was roundly ignored by everyone. She wound up being the main architect of a consumer advocacy agency designed to prevent such a thing from happening again.
Likewise in the UK, Liberal Democrat MP Dr Vince Cable (that doctorate is a PHD in economics), spend the later years of the Blair government and the early years of the Brown one warning of "casino banking" exposing the London Stock Exchange and UK banking sector to huge risk. Cue the 2008 financial meltdown, and the eventual election of the current Coalition government in 2010. He's now the Rt. Hon Secretary of State for business. The Trope is them redoubled as large parts of the Conservative Party choose to ignore him because he's from the Liberal Democrat Party. (Politics can be messy.)
Slightly subverted by Hussein Kamil Hassan al-Majid, Saddam's son-in-law and head of Iraq's WMD program. His statements about the progress Iraq's WMD programs had made surprised intelligence agencies but was accepted. His statements that Iraq's WMD were destroyed on the other hand...
The UN Weapons Inspectors who went into Iraq in 2002-2003 would fit as well. They pointed out that many claims of Iraq possessing WMD were invalid or wrong. After saying they needed a few months to continue inspections, they were ordered to leave (not by Iraq, but by the US) in 2003...
General Billy Mitchell who, in 1924, prophesied a war between the Japanese Empire and the USA over the two's interests in China and the Pacific. He also predicted that it would be the Empire who would strike first, much as they had done in the Russo-Japanese war of '04-'05.
Likewise, US Admiral Harry Yarnell proved in a war game in 1932 that Pearl Harbour was vulnerable to an aerial (sneak) attack. However, his superiors dismissed his findings and were proven wrong the hard way in 1941 when the Imperial Navy's air forces used the same approaches that Yarnell had used to attack the fleet at anchor there, to devastating but somewhat ephemeral effect.
On the other side, when the USA placed crippling sanctions upon the Empire of Japan to protest their occupation of French Indochina (and implicitly, their continued war upon China), the Japanese cabinet refused to consider negotiating seriously on withdrawing Japan's forces. Instead, the Navy pushed to implement its Southern Attack Plan — which entailed, by necessity, declaring war on the Netherlands, Britain and America. The man they chose to orchestrate their attack upon the USA's fleet, Admiral Isoroku Yamamoto, explicitly told his superiors that the plan was fatally flawed. He understood that a war with the USA would not be like the war with Russia — the former was far more powerful relative to Japan than the latter had been. He predicted that the USA's 'massive' financial-industrial advantage (of about ten-to-one, which is even greater than it sounds because of the greater efficiency involved in economies of scale) would start to show within just six months of the start of a war with them. His exact words, in fact were: "I will be able to run wild for six months to a year at the outside. After that, I can give no guarantees." Japan attacked Pearl Harbor on December 7, 1941. The Battle of Midway, where Japan lost the cream of her carrier fleet, and which can be seen as the high-water mark of Japanese expansion during the war, ended on June 7, 1942 — exactly six months to the day of Pearl Harbor. Of course, US victory was inevitable — even if the Empire had won a devastating victory at Midway and went on to win another three battles just like it the USA would eventually have spammed its way to victory, anyways. The USA's production of aircraft carriers and capital ships actually dropped right off after 1943 as they belatedly realised they had basically won already and didn't need any more.
John O'Neil, an FBI agent who basically saw the War On Terror (including the 9/11 attacks) coming roughly a decade ahead of time but was ignored. In a fit of tragic irony, he ended up working as security of the World Trade Center and ended up dying in the same attacks he predicted.
In 1865, George Goyder drew a line splitting Australia into areas suited and unsuited for farming. He based it on sound observations of the vegetation, but farmers settled anyway due to high rainfall for the previous few years. Then they had to vacate when the rains stopped and the land became just as dry and useless as he said it would.
This was possibly the cause of the fall of the Roman Empire before it even became an empire — that is, the empire may have been doomed before it was formed. In the 2nd century BC, two brothers named Tiberius and Gaius Gracchus realized that Rome's military model was unsustainable in the long term. They pushed for reforms in the Senate, but their ideas were unpopular (since they would adversely affect the rich landowners who controlled the Senate) and their attempts to push these reforms led to their murders (one was beaten to death by the senate). Not long after that, the Gracchi's fears soon came to pass. A man named Gaius Marius was assigned to raise an army, only to find that there just weren't enough qualified troops in all of Italy. For instance, Rome's laws required soldiers to own land, but all the land was owned by a handful of people, which was exactly the sort of thing the Gracchi foresaw. Marius reformed the army to eliminate some of these requirements, but even his reforms only slowed Rome's decline rather than stopping it.
Thankfully averted by Dr. Frances Oldham Kelsey of the FDA in regards to Thalidomide. She'd insisted on further testing before granting the drug approval for US distribution, holding out for long enough that the horrendous birth defects link became well-documented, earning Kelsey a medal from President Kennedy, and later an award named in her honor.