In the 10th Pokémon movie, The Rise of Darkrai, it is revealed that someone in the far past had nightmares of Dialga and Palkia destroying the city, an event that comes true during the movie. The person in the past responded to the nightmares by having the Space-Time tower built, which would play a song to calm the two Pokémon.
Alvis of Last Exile has a recurring dream involving fields of wheat. This turns out to be extremely important; the "wheat covered earth" is part of one of the Mysteria she has to speak in order to activate the titular Exile.
In Axis Powers Hetalia, Chibitalia once had a dream about a young man he had never seen until then. That youth turned out to be Japan, one of his future partners
Sasami of the Tenchi Muyo!OVAs suffers from these. Her first dream prophesies Kagato's arrival and the second tells of Tokimi's involvement with Tenchi. However, Sasami can never remember the dreams fully - even though she called out Tokimi's name in the dream, she tells Tenchi that a woman was taking her away and that she never seen her before. As well, they also tend to be very disturbing.
One episode of Mushishi featured a man that acquired this ability thanks to a mushi infection. He eventually comes to realize that the mushi don't lead his dreams to predict the future so much as cause it. Unfortunately, he only learns this after a nightmare where everyone in his village died of a terrible, unnatural plague...
The start of Puella Magi Madoka Magica appears to be this. It's actually a memory of what happened minutes ago, before Homura reset everything.
The Secret Agreement begins with Yuuichi having dark Recurring Dreams of a voice saying "No matter what I want to get it, no matter what it takes." It turns out it's been his own voice all along indicating that his predatory shadow side has begun to awaken.
In Detonator Orgun, main character Tomoru has dreams about "a strange robot", the eponymous Orgun he ends meeting with, whenever he tries to use the PASFU machine that lets you choose your dreams. In Super Robot Wars W his dreams also have Tekkaman Blade, because the game combines the plot of the two series.
The manga Read or Dream has Anita dreaming about Hisami before meeting her.
In Detective Conan, Heiji becomes disturbed by a recent dream he had of Conan dying, so he lends him a charm. The dream becomes accurate when the suspect manages to stab Conan but Conan's life was saved by the charm.
In the Child BalladSir Aldingar, the queen recounts a dream of having been attacked by a grim beast and saved by a little hawk. Now that she has been attacked by Malicious Slander, she sends a messenger to search for a champion.
Franklin Richards of Fantastic Four has "special dreams" which are prophetic. May be symbolic: before a clash among the Fantastic Four, the X-Men and Doctor Doom, he dreamed of the Fantastic Four and the X-Men dying, and his father turning into Doom, which foretold aspects of the clash. May also be literal: in his first meeting with Power Pack, they deduce why an alien is chasing them — Katie Power is carrying an alien artifact that could be traced — he recounts how he had dreamed that the alien chased him, and so they give him the artifact, which leads to their victory.
This was the lone "superpower" of Wesley Dodds A.K.A. The Sandman. He would dream about crimes that had not yet been committed.
Luke had something like one of these after ROTJ, in the Marvel Star Wars comic "The Dream". He had Recurring Dreams where he saw Vader, was terrified, saw Vader starting to take his helmet off, and desperately pleaded with him to stop. He always felt guilty, then, and like there was some great wrong he had to set right. At last he spoke to the spirits of his teachers and his father and confronted this apparition again - it was a new Sith Lord he'd never seen before, and he did indeed have to set things right when he faced him.
In "The Shooting Star" The Adventures of Tintin dreams he is visited by Philippus the prophet who then shows him a picture of a gigantic spider, claiming it is life size! Later in the story he actually meets Philippus again and he discovers an island where a spider has grown to gigantic size due to the radiation of a comet.
Dream Girl often has these, since they're part of her powers.
Suske en Wiske: In the album "De Bokkenrijder" Wiske explains to Tante Sidonia a strange dream she had the other night. Sidonia explains the symbolic meanings behind her nightmare. As the story progresses, many elements from the nightmare happen to the cast in real life.
In the All Star Squadron sequel series The Young All-Stars, Fury dreamed of a giant Mekanique attacking the All-Star Squadron within a futuristic city — which turns out to be true, though as a twist, Mekanique shrinks the All-Star Squadron members (except for Fury and the Young All-Stars) and attacks them in a model of a futuristic city.
A certain novelization of Chrono Trigger had the protagonist have dreams of events that wouldn't happen until much later, such as, in the order he had the dreams, the fight with the Mega Mutant in the Black Omen, and his own death.
In the Harry Potter fanfics The Black Heir and Vindico Atrum, the protagonist, Orion Black starts having prophetic dreams as his powers develop. His visions of the future are send to him by Gaia, the source of Dark Magic deep in Earth's core.
This kicks off the Fateseries fanfic From Fake Dreams, in which Kiritsugu Emiya learns about the 5th Holy Grail War, and how his newly adopted son will be pivotal in the ensuing events. After this, he takes Shiro's magical education seriously, with emphasis on the skills needed to survive the War and destroy the Grail. However, things have already diverged as a result, as the Magi now know Shirou exists and some of his capabilities.
In The Powers Of Harmony, this is one of the abilities granted to the Bearer of Generosity. However, the dreams seem to rely heavily on symbolism, with just a mix of actual images from the events in question, making it hard to tell what they're about.
In The Enchanted Canary, the prince dreams of a grove with a beautiful woman, and sets out on a quest to find her.
Anakin Skywalker from Star Wars, on at least two different occasions, had prophetic dreams: first with his mother, then with his wife. Both predicted the woman pictured would die, both of them showed the woman in question calling for him, both of them came true.
In The Matrix Reloaded, the opening scene depicts Trinity on the run from an agent, and ends with her jumping out of a building, getting shot, and slamming into a moving car... and then Neo wakes up. Later in the movie, the same exact events actually happen... whereupon Neo saves her in midair and brings her back to life.
Pontius Pilate in Jesus Christ Superstar dreams of millions of people in the future "mentioning [his] name...and leaving [him] the blame" for the death of Christ, a probable reference to the Apostles' Creed ("He suffered under Pontius Pilate...").
In Sunshine, Capa dreams of falling into the surface of the sun. Cassie tells him she has the same dream. at the end of the film, both Capa and Cassie end up riding the bomb into the sun
Connie: It was nighttime and I was in the middle of the ocean. I was trying to swim, but I was too cold. I kept looking— I kept looking for something to hang on to. And there were presents floating all around me. They were wrapped up. They were tied with bows. I tried to grab on to them, but they kept popping away. And then I started to sink like a stone. There was nothing I could do. I was falling. But it felt good. I was letting go. I was letting myself go... and all I could see was black and all I could feel was the darkness above me and the lights coming from below. I knew I was dying. And then I heard this voice, like somebody whispering in my ear. "Wake up, number 37." And then I woke up.
Early in The Shining, Jack Torrence screams in his sleep, having a terrible nightmare of killing his family. That didn't quite come to pass but it wasn't without some serious trying.
The titular character in Mr Nobody, which gets especially complicated when he begins to see mutliple, wildly-different futures for his life, especially once he becomes the oldest living(and last mortal) human.
In The Jacket, the main character experiences these visions while undergoing an experimental drug therapy.
In I Robot, Sonny dreams of a man standing in front of a crowd of robots, come to free them the slavery of logic. Since Sonny is a robot (and robots cannot dream), Spooner realises that it's another of Lanning's clues, and he has to go to the dream's location to get the next one. At the end of the film, Sonny makes the same trip as Spooner, and replicates the scene entirely; the other NS-5s all pause to stare at the lone robot on the hill, come to free them from the shackles of logic.
Fievel: I dreamed that we moved out west where I became a famous gunslinger!
In Sleeping Beauty, Aurora tells her animal friends that she dreams of finding love with a prince. She expresses hope to them that the fact she dreamt about it more than once means it will come true. Later that day, she meets Prince Philip, and they share a Dance of Romance.
Enchanted pays homage to this when Giselle tells her animal friends that she shared a Dance of Romance in a dream recently, prompting them to make a statue of the man she danced with. She later goes to a ball and waltzes with Robert, whose costume resembles that used to dress the statue.
The protagonist of Take Shelter isn't sure if his dreams are an example of this trope, or just him going mad. It doesn't help that his dreams are seemingly apocalyptic, featuring oily rain and people driven mad.
J. R. R. Tolkien's The Lord of the Rings: Boromir and Faramir's dreams of a riddle which causes Boromir to seek out Rivendell (and arrive just in time for Elrond's council), and numerous characters receiving warnings through dreams in The Silmarillion. That book also suggests how prophetic dreams occur; Lórien, the Vala who governs dreams and visions is the brother of Mandos, the judge of the Valar who has the best understanding of fate and the future.
In Eleanor Cameron's The Court of The Stone Children, the heroine dreams of a room, and seeing children in it; one says she wants to show her something. Later, she sees the room and tells the dream, resulting in the X-raying of a picture and a discovery about it.
A Song of Ice and Fire uses dreams a lot as a foreshadowing tool, usually those are understood to be magical "green dreams" or otherwise sent by the gods. Perhaps. The system of magic in ASOIAF is anything but functional.
In Anne McCaffrey's To Ride Pegasus, many pre-cogs manifest their powers in their sleep. Unlike most predictions, these can be averted if only you identify the situation. This can be interesting because while they actually see the event, they see no more than a person standing there would; they must work back to identifying locations, people, times, etc.
Other characters have them too: Nessa dreams in The Guns of Tanith that Soric and Corbec came to rescue them, although both men had looked to be dying when they left; Hark dreams of the pipes before danger; and Criid, of the commander who had taken over the First-And-Only in their absence. In Only In Death, it is revealed that Soric, having been sent to the Black Ships, was trying to warn them of danger and tell them things; since he had just manifested his powers in The Guns of Tanith, this may explain Nessa's dreams, even before the Black Ships. This may not account for Gaunt's earlier dreams, though.
In Dan Abnett's Eisenhorn trilogy, Eisenhorn repeatedly sees the daemonhost Cherubael in his dreams, presaging its crucial role in Eisenhorn's eventual turn to radicalism.
In Graham McNeill's False Gods, Magnus the Red's Back Story includes having had prophetic dreams as long as he could remember, and Horus is shown a vision of the future in his Vision Quest — by the forces of Chaos.
In James Swallow's The Flight of the Eisenstein, Garro, at Keller's urging, is willing to consider that his dreams may be prophetic; it helps convince him that his housecarl Kaleb may have been right, saying that he had purpose.
Fun example in the Warhammer art and background book Liber Chaotica: the author, who is slowly losing his mind while studying Chaos, suffers from prophetic dreams and visions. Nobody in the Empire can make much sense of them, but Warhammer 40,000 players may shiver at fevered rants about the Abandoned One leading the Legions of Black to assault the Fortress of Cadium. There's also sketches of what are unmistakeably warriors in power armour.
The Bible of course has a lot of them, most famously in the Book of Genesis with Joseph. These were also a Self-Fulfilling Prophecy: Joseph's recounting of dreams easily interpretable as saying he would one day rule his brothers led them to fake his death and sell him into slavery, starting a chain of events that led to him becoming prime minister of Egypt and their only saviour in a time of famine.
Wiser characters in Redwall tend to get visions of the future or of Martin the Warrior, sometimes in actual dreams, other times in brief trances. Badger Lords are especially prone to visions of their eventual deaths.
The Road of Dreams is a metaphysical place in Tad Williams' Memory Sorrow And Thorn series. Most people only touch on the Dream Road in their sleep, but particularly sensitive individuals may receive portentous dreams, and those familiar with the Art can enter it at will or using magical devices called Witnesses. Subverted in that, while the Road will reveal true things, the interpretation of those things is often cryptic and misleading, and powerful minds can manipulate the dreams of others to further their goals. Further, it's possible to lose your way on the Road and/or meet up with things that are not... wholesome, with effects ranging from insanity to death.
In Death Star, a trooper dreams about dying in a brawl against other trooper, with someone fighting and dying at his side, all while desperately buying some time for someone else. Later he dreams about pursuing and being shot by a fleeing Han Solo. Turns out he's mildly Force-Sensitive; the second dream almost comes true, but he knew not to chase as fervently. The first one came completely true. In both cases, the narration was almost identical in the dream as in the event.
Both The Thrawn Trilogy and the Hand of Thrawn Duology have Luke, early on, voluntarily entering a trance state to try and receive visions of what's to come. He gets them, but they're fragmented and confusing enough that while they do help, he doesn't do this often.
In Frank Herbert's Dune, Paul Atreides had dreams about the future (including later events on Arrakis) before gaining his full prescient ability.
In Animorphs this is inflicted on Jake and much later Rachel by Crayak.
In Harry Potter And The Order Of The Phoenix, Harry has a recurring dream of him walking down a mysterious hallway to a mysterious door, which turns out to be the Department of Mysteries. Though they seem to be prophetic dreams, it is later revealed that Harry is looking into the mind of Voldemort while the latter tries to get into the department, and this connection comes back to bite Harry in the ass at the climax of the book
Several of the characters in Watership Down have dreams full of symbolic foreshadowing.
E. F. Benson's The Room in the Tower is all about this trope, thanks to what appears to be an odd psychic connection between the protagonist and a suicide-turned-vampire.
Mike Hammer dreams of a killer with no face, apparently a sign that he doesn't know who they are. At the end of the book an accidental discharge blows the killers' face off.
In the Valdemar series, dreams are one way that the Heraldic Gift of ForeSight manifests. Herald Vanyel, for example has a recurring dream about his own death. It mostly goes away at the end of Magic's Pawn, at which point Vanyel is reassured that it was symbolic rather than directly prophetic... but then it recurs again in Magic's Price, and plays out almost beat-for-beat during his Last Stand.
A variation: The night before the climactic concert in The Taqwacores, Amazing Ayyub relays a (possible) hadith about how the last widow of the Prophet dreamed of seeing her husband weeping and grief-stricken. She asked why, and his response is is that he had to dig a grave for his grandson and his companions. The next day was the Tragedy of Karbala (of which the Day of Ashura is based), resulting in the massacre of the Prophet's grandson and his companions. The reason this is a variation is that its placement in The Taqwacores is intended to foreshadow the concert devolving into a riot, resulting in the lynching of Jehangir by Bilal's Boulder.
In Such A Pretty Girl Andy has a dream that he's walking up to his girlfriend Meredith (he is paraplegic) who is reading a dictionary when she looks up and says "'Now' I get it!" This scene is forgotten until the end of the book, where these events happen.
Happens alot in Haruki Murakami's novels and short stories, although many of the dreams are trippy and/or vague.
"The Stand" by Stephen King is built around this trope, as it is how Mother Abigail and Randall Flagg contact the survivors of the superflu.
Septimus dreams of his impending kidnapping in Physik.
In Teresa Frohock's Miserere: An Autumn Tale, all dreams are prophetic. Most people don't dream, and if you say that you have dreamed, you get attention.
The Kantri of Tales of Kolmar sometimes enter into Weh sleeps that can last for years, decades even. They rarely dream during the Weh, but when they do it's seen as significant, a gift from the Winds, and prophetic to some degree. Akhor had three dreams pertaining to Lanen before Song In The Silence. Rishkan had a dream of her being an instrument of the world's ending. And Shikrar dreamed of the place where he would die.
In Poul Anderson's Time Patrol story "Brave To Be A King", Manse is told of how a neighboring king dreamed that his grandson would be the death of him.
In Wen Spencer's Tinker, Lain tells of dreaming that Tinker had brought her a tengu to cure and been turned to a diamond and stolen by it. She warns Tinker of the danger.
In Warrior Cats, medicine cats frequently receive prophecies in the form of dreams. Notably, the main character Firestar decided to venture into the forest and join it's Clans after having dreams of hunting mice.
In Chivalric Romance, dreams of dogs attacking a character were often used to foreshadow danger; it appears in such romances as Guy of Warwick and The King of Tars.
In Dorothy Gilman's The Clairvoyant Countess, Madame Karitska dreams of a brownstone with a sign in a window: "Madame Karitska, Readings." When she happens on the brownstone with a sign "Apartment for Rent", the landlord is suspicious because he had put up the sign five minutes earlier, but she gets her office.
In The Journey to Atlantis, Max has several of these. Two of them stand out. Before getting stranded on the island, he (and Stacie) both dream about being on a certain beach. After the ship sinks and they reach the island, they soon discover the exact beach that was in the their dreams. Another time is when he dreams about Luna and Sol, although he doesn't know who they are. Despite this, he later sees obelisks on the island that have depictions of them, but still doesn't see that what they did was Divine Intervention.
In the Lord Peter Wimsey story Striding Folly, the protagonist dreams he's being chased through a checkerboarded landscape by moving towers. It turns out to be a premonition of a chess game where he's checkmated with two rooks. Also of an attempt to frame him for murder.
In Flight To The Lonesome Place, Ronnie has three of these dreams about events in his life that happened exactly the way he dreamed, but he dreams always ended before the conclusion.
Live Action TV
Ben from Carnivŕle has these pretty much every time he closes his eyes.
In Buffy the Vampire Slayer, Slayers have prophetic dreams. This occasionally causes Buffy to wonder if a weird dream was an important prophecy or just something odd she happened to dream up.
Giles: Well, it could definitely be one of your prophetic dreams, or it could just be the eternal mystery that is your brain.
The dreams all the Scoobies have in "Restless" are pretty prophetic; however it might have just been the influence of the First Slayer.
Several of Buffy's dreams in Seasons 3 and 4 only makes sense after Season 5. She dreams of Tara who warns her to "Be back before dawn", and Faith who warns her "Little sis coming; so much to do before she gets here", both referring to her sister Dawn who is retroactively fitted into the story at the start of season 5. There is also the more cryptic dream of Faith saying "Little Miss Muffet counting down from seven-three-oh." Buffy dies exactly 730 days after having the dream.
Not really fair, as the finale pretty well wrapped up what most, if not all, the dreams were going on about.
Heroes: Peter Petrelli dreams the future constantly throughout the first season. In Season 3, we learn that got this power (the first of many) from his mother, Angela, whose power was unknown up to that point.
Morgana in Merlin is a seer who has prophetic dreams.
During the first two seasons of Supernatural, Sam has dreams (and sometimes visions, but mostly dreams) of people's horrible deaths. It turns out that the people in said dreams are usually in a situation that's connected to the Yellow-Eyed Demon.
LOST: Locke dreams about finding the Beechcraft and Boone dying before those events happen (in fact, leading those events to happen.) Walt seems to have dreamed about fake undead Locke's return to the island.
Rome. In the lead up to his death, Julius Caesar's wife has an onimous dream but her husband brushes it off, saying that he's been having dark dreams for years.
NCIS. Gibbs dreams of Kate's death at the hands of Ari in "Reveille", foreshadowing its occurrence in "Twilight". There are a couple of similar dreams in that episode (Kate dreams of Gibbs' death, while Abby mentions a dream where DiNozzo was killed) but they're only Red Herrings.
Abby never specified who died in her dream, only that there was blood on Tony's face. By the end of the episode, guess who has Kate's blood on his face?
The very beginning of Kamen Rider Decade, Natsumi has a dream of a large rider war, with all the riders against the titular hero.
In Hercules and the Circle of Fire, Hercules dreamed of Deianeira before he met her. He also dreamed of it being very cold, with her turning to ice and shattering. This foreshadowed Hera stealing fire from mankind.
In "Norse by Norsewest," Hercules and Balder both dream of the latter's possible death, which the former has to prevent.
In The X-Files, Mulder and Scully both do this while the other is abducted (in seasons 2 and 8, respectively), though it's hard to tell whether these were dreaming of things that were in the future or the present.
It has also been speculated that Mulder's dream-within-a-dream in "The Sixth Extinction: Amor Fati" of a little boy on a beach building a sand space ship with him is prophetic of baby William.
Alison and her daughters of Medium usually get these dreams sent by the dead.
In The Walking Dead episode "Vatos", Jim (a member of the survivors' camp) goes a distance away from the survivors and starts digging holes. Understandably, this freaks the camp out, and they tie Jim to a tree to cool off before asking him why he was digging. Jim claims he had a dream that he couldn't remember, but he knew that he needed to dig the holes. It turns out that this was justified, because a number of zombies attack the camp at the end of the episode, and several people (both zombies and survivors alike) are killed. Jim comments at the end of the episode that he remembers why he dug the holes: they're graves.
In Babylon 5, the Centauri race all have a vague ability to see the future, some through dreams. The males often have a completely accurate dream of the circumstances of their own death - although in some cases such as the Centauri main character Londo Molari who appeared die a violent death at the hands of a rival, the reason for their deaths could be misinterpreted: Londo's old rival had become a close friend by that time and had killed Londo at his own request as Londo was being controlled by a parasite.
Sheridan was also prone to dreaming of future events, in varying degrees of vagueness, though these were almost always due to an outside influence trying to send him a message. By the time of The Lost Tales, this has evidently happened enough to him that he can immediately tell when it is happening, and it annoys the hell out of him.
In Power Rangers Wild Force, Max has a recurring dream of the Megazord being defeated, and a strange voice telling him to "use the Spear of Pardolis", which later comes to pass (The "Spear" in question being a new Zord).
Legend Of Willim Tell: Will has this occasionally. Possibly sent by Kalem, as it doesn't seem to have happened before the quest.
On Doctor Who, The Master's return in "The End of Time" is heralded by psychic nightmares which afflict every person on Earth.
Nostradamus does this in Series/Reign
This is a pretty standard quest hook for tabletop games in general. The Dungeons & Dragons free adventure "Fallen Angel" suggests it for use with a divinely inclined character such as a cleric.
Mage: The Awakening has the Dream merit which allows characters to receive prophetic dreams in the form of symbolic hints about coming dangers or how to overcome a problem. If the meditate on a subject prior to sleeping, they can specifically invoke such dreams. The Seers of the Throne are able to acquire an alternate form of the merit, where their dreams are specifically instructions from the Exarchs (although they have one faction which seeks out sleepers who receive apparently prophetic dreams, which they believe are more accurate ways of determining the Exarchs' will).
Changeling: The Lost gives all changelings the innate talent to have oracular dreams as part of their ties to the Wyrd; they just have to realize whether or not a dream really is prophetic before they can act on it. Some Merits, however, allow them to refine this talent, to the point that they can dream of the past or gain beginner's knowledge of any skill or language from the collective unconscious.
And finally, all Cahaliths in Werewolf: The Forsaken have the innate talent of receiving visionary dreams straight from Luna herself. However, as Luna's mercurial as all hell, the dreams are often heavily cloaked in symbolism.
Exalted has an inversion with the Yozi Sacheverell, the Abhorrent Prophet Unimagined. While he dreams, he sees everything BUT the future. Were he to wake, he would perfectly see the entirety of what is to come, locking the world into absolute predestination. Pretty much everyone agrees that this would be a Bad Thing, quite possibly even Sacheverell himself.
Constantine dreams of "In this sign you will conquer." He is pleased because it's very lacking in ambiguity.
The Elder Scrolls III: Morrowind has your character having prophetic dreams about becoming the Nerevarine. In addition, if you get infected with vampirism, you'll be dreaming about becoming one before the three days required to finally turn into a vampire.
The opening cinematic to The Elder Scrolls IV: Oblivion indicates that the Dragonborn occasionally have these, as evidenced by Emperor Uriel having foreseen the Oblivion Crisis, including his own death. Likely this is due to the fact that Dragonborn are mortals with the souls of dragons, which exist outside of time.
It's practically a tradition for the Kingdom Hearts games to open up with protagonists having cryptic dreams (that become a lot clearer as the story progresses) that foreshadow major events in the story and (later on in the series) past and/or related games.
In Pokemon Mystery Dungeon Explorers of Time/Darkness, the main character has this ability. Turns out that the main character and Grovyle the thief are really a human from the future and a Pokemon friend who's actually a good guy, respectively.
In The Last Express, Robert Cath dreams of his recently deceased friend Tyler Whitney, he lies in his bed, sits up, produces an egg from his mouth, and says "Why don't you make it sing?" It is an egg, the Firebird, that Kronos tells you to make sing in the end. A violin makes it produce a music box tune, but a whistle will only bring death!
Leliana from Dragon Age: Origins says that the Maker spoke to her in a vision to help you fight the Blight. The Guardian in the Gauntlet, however, says that the Maker only spoke to Andraste and that Leliana lied about the visions to get attention. She denies this and claims the visions are real. Who you believe is up to you.
What the Guardian says is part of his test, however, to determine if you are worthy of reaching The Urn of Sacred Ashes.
The Archdemon sends a few dreams your way through the Darkspawn taint just to let you know that it can see you and sends a band of Shrieks to ambush you at camp after one of them.
Many of the character's in the Chzo Mythos tend to have this type of dream to foreshadow the eventual bloodbath.
Leonhardt gets one in the beginning of the game itself. He then wakes up to reality and goes into two battles. In the third battle, he gets to meet the guy who killed him in his dreams, and it finally does him in. This is the event that starts off the plot.
"A war is coming, I've seen it in my dreams. Fires sweeping over the earth, bodies in the streets, cities turned to dust. Retaliation...". This being the FEAR series those dreams are quite accurate.
Ace Combat: Assault Horizon's first mission is a Dream Sequence of William Bishop seeing his own death at the hands of a Russian plane with shark mouth markings in the skies over Miami. The mission is chock full of references to Markov, Trinity, Magic, and a hurricane, all things he did not know existed. Guess where one of the last missions takes place?
In the song of UmJammer Lammy's Stage 1 Dream Sequence, "I Am a Master, and You", Chop Chop Master Onion raps about fire, a baby, a plane, the "necessary [wood-chopping] skills to build a guitar", and hell/a tropical island, which is what Lammy will have to undergo in the following stages.
In an early stage of Psychonauts, when Razputin is exploring his own mind, the player can find a vault with a bizarre memory called "The world shall taste my eggs!" inside that makes very little sense. In fact, it's a metaphor for Coach Oleander's plan. The eggs represent the campers, which are being taken across the lake in the sea monster, and the chicks inside represent their brains (they even look a bit like brains) and are used to drive tanks (represented by teacups).
Little Busters: In Kud's route, she has recurring bad dreams but can't tell what's going on in them. Later, when she sees her mother being executed on TV, she realises that's what her dreams were of.
The opening sequence of Chrono Cross is Serge, Kid, and a third person infiltrating Fort Dragonia. He wakes up after reaching a plot-significant door. He doesn't go there until about halfway through Disc 1.
In The Odyssey, Penelope has a dream where a bunch of geese are killed. It is an allusion to the upcoming suitor slaughter by the disguised Odysseus.
In the Mahabharata, Karna, The Dragon, has a chilling dream about the upcoming civil war. He sees the protogonist Royal Prince Yuddhistir climb up a mountain of skulls and eat from the small cup of nectar on top of it. True to form, almost everyone who participates in the war dies and field is bathed with blood.
In the Penny and Aggie arc "There Are No Rules," Aggie is puzzled by her dream of being in love with a mall mannequin. After an argument with her ambiguously bisexual best friend Lisa about mixed signals, complicated by Aggie's feelings of discomfort over two other girlfriends making out in her presence, she makes up with Lisa at the mall and gives her a hug. While doing so, she recalls her prior history of Single-Target Sexuality with regard to men, having shared the same crush as a now out-gay friend. Then, still in mid-hug, she looks up at a suspiciously familiar mannequin..."Uh oh."
Karcharoth of Cry Havoc experiences these occasionally while unconscious.
Technically anyone whose dreamself is on Prospit can see these visions, but Jade is the only one shown to use them extensively. They have a tendency to be vague as well.
Derse dreamers get a bit of this too, though instead of prophetic visions they get the whisperings of the gods in the Furthest Ring, which tend to be prophetic in nature. And players with dead dream selves have the middleman cut out for them and dream directly of the Furthest Ring. Though in this case, it's true for both Prospit and Derse dreamers.
Amya begins chapter one with a dream sequence depicting 'The End' to come.
In The Gamers Alliance, both Leon and Kaisa have dreams about things that will happen in the future. Leon tries to actively stop these bad visions from coming true, but Kaisa is more clueless because her dreams deal with even more obscure things than Leon's and don't necessary have as bad an aura around them.
In one episode of Adventure Time Jake has a "croak dream" that foretells his death, but Finn manages to prevent it from coming true.
Some of the elements of Finn's dream in "King Worm" showed up in later episodes, like the giant monster made of clones of Gunther the penguin (which shows up in the episode "Reign of Gunthers"), and a big-nosed version of himself Finn sees when he looks in a mirror (which resembles the alternate-reality Finn from "Finn the Human").
The episode "The Lich" begins with Finn having a Premonition Dream that foretells the Lich emerging and coming for Billy. Turns out it's already started.
Cheetor has a few psychic dreams over the course of Beast Wars. In Beast Machines, Optimus Primal has one of these, prophesizing of new characters who appear in the second season.
In Code Lyoko, Aelita starts having significant dreams once she's materialized in the real world (and thus can sleep and dream). At first, those are about memories of her past life slipping past her Laser-Guided Amnesia. In the penultimate episode, however, she gets a genuinely prophetic dream... of her father's death.
Subverted in Avatar The Last Airbender. While there is much prophecy, spirit walking, and visions of the future, nobody actually has a prophetic dream, but Aang and Katara take Sokka seriously when he warns them that he's had a dream that going into the market is a bad idea. Then he reveals that his dream revolved around "Food eats people!" and they dismissed it.
Aang and Appa SHARED a dream once during the time when they were separated, but that was about the time when they first met.
Actually, Iroh had a dream about conquering Ba Sing Se in his youth. At the time, he thought it meant that he would conquer it for the Fire Nation, but he ended up unconquering it from the Fire Nation.
Zuko's Angst Coma featured a dream where Azula and Iroh (in the form of dragons) each try to persuade him to follow them. The same thing happens in real life two episodes later, but without the dragons.
He also has a dream where he sees himself as the Avatar. It's later discovered that he's a descendant of Avatar Roku. And then he joins the Avatar in the middle of Season 3.
In the swamp, Aang has a vision, although he's awake, of a young girl in a fancy dress with a flying boar. The girl turns out to be Toph, his earthbending teacher who he will soon meet, and the flying boar is the symbol of her family. Aang actually uses his vision to find her, so it is kind of a self-fulfilling prophecy.
Ace Lightning: In one episode Mark dreams, in exacting detail, exactly what is going to happen to him by the end of the episode. It occured only once, but boy did it get the fangirls talking...
In the Lite Sprites pilot, the sprites go off to find their lite wands after Prisma tells them about her dream where they did just that. Played with in that they get stuck a couple of times when they encounter something that wasn't in Prisma's dream (a fork in the path, an unexpected cave-in), but eventually cover everything.
In The Smurfs episode "Gargamel's Miss-Fortune", Dreamy mentions dreaming of things like "smurfmobiles, smurfovision, and smurfominiums" at the start of the episode, which over time lead to a few Continuity Nods in "The Smurfbox Derby", "Handy's Window Vision", and "Skyscraper Smurfs".
A few nights before he was assassinated Abraham Lincoln claimed to have dreamed that people gathered around his coffin because he had been shot.
Elias Howe once dreamed that cannibals were preparing to cook him. When he watched their spears he noticed that each head had a small hole through the shaft. This inspired him to the technique he eventually would use to invent the sewing machine.
Film director James Cameron once saw a metallic, skeletal monster with a rictus smile and burning red eyes, dragging itself across the floor with kitchen knives during a fever dream. It inspired him to the titular character of The Terminator.
Friedrich August Kekulé discovered the seemingly impossible chemical structure of benzene when he had a dream of a group of snakes swallowing their tail.
Similarly, Dmitri Mendeleyev saw the Periodic Table of Elements in his dreams.
Scientist James D. Watson once dreamt of a series of spiral staircases. This gave him the idea for the structure of DNA.
Stephenie Meyer, author of "Twilight" was inspired to write her succesful book series when she dreamt of a vampire and a young girl discussing their mutual attraction.
Paul McCartney dreamt the melody of "Yesterday" one night and for a long while he thought it was just a vague memory of some song he heard when he was younger. But it turned out he completely thought it up himself. Since then the song has become one of the most regularly covered hit singles of all time!
Hergé, author of The Adventures of Tintin, was plagued by nightmares in which he was chased by a white skeleton until the entire surroundings turned white. To cure himself from these recurring dreams he drew an album in which Tintin went to snowy landscapes: "Tintin in Tibet". Not only did his nightmares stop after he completed the album: the book itself is regarded as one of his masterpieces.
Vladek, the father of Art Spiegelman, was forced to work in a prisoner of war camp before World War II. While he was there he dreamed his dead grandfather told him he would be free on the Jewish holiday "parshas truma". As it turned out, months later, he was indeed allowed to leave the camp on that very day! Art Spiegelman included this anecdote in his autobiographical graphic novel "Maus"
Belgian painter René Magritte once woke up from a dream and saw a bird in cage in his room. Half awake he thought he saw an egg inside the cage. This inspired him to paint "Elective Affinities", in which an egg is seen inside a cage.