Narumi Kiyotaka from the Spiral manga, even more obviously bored in the prequel Spiral: Alive. It is hinted that the events of the manga happen because he was just too bored, and stated to be the reason he acts like an idiot and does ridiculous things such as dressing up in furry costumes: to spice things up in his boring life. Although his ability to predict everything is presented more as a form of incredibly high intellect than a supernatural ability to see the future, he is still considered a "god" by everybody else. Ayumu eventually outwits and defeats him, but Kiyotaka is so enigmatic it can be argued he knew and in fact arranged this outcome. There's no way to know for sure.
The interfaces from Haruhi Suzumiya. The desire to avert this is likely what drove Ryoko into the radical faction of the entity, and Kyon notes in the novels that Yuki becomes noticeably happier after she loses this ability.
Steins;Gate: Okabe quickly discovers that Mayuri's death is inevitable in any world-line other than the original. The knowledge that whatever he does will lead to her death every time takes a serious toll on his psyche.
Sort of example/subversion: The Midnighter has a huge amount of advanced circuitry in his head that allows him to run any battle a million times in his head, ensuring victory. The only two times he can't predict the fight, he's understandably shaken. (The first time, it's against a guy who does nothing at all, so he can't react; the second time, he's against The Joker, and has no idea what he's going to do.)
Dr. Manhattan in Watchmen. His reaction is to stop caring what happens. When a tachyon swarm disrupts his ability to see the future, he becomes excited, saying that he'd almost forgotten how wonderful it was not to know what was going to happen next.
It's never made clear whether or not he has no ability to change the future, however. Because he stops caring about the passage of time and life, he never attempts to: so you get scenes wherein he entertains the idea of interfering but doesn't specifically because he's already seen he doesn't, rather than because he can't. He definitely believes that he doesn't, though, and so does nobody else.
Which is possibly part of the conundrum. He knows he will not care enough to alter an event hence he doesn't. To illustrate, perhaps Silk Spectre also has the ability to change the future at any given point by simply physically walking in a different direction from Manhattan's vision but she just won't. In a sense, everyone and no one can change the future.
In Runaways Niko inflicts this on Gert's parents when she encounters them in the past. Consequently they both know that the course of action they're taking will lead to their own and their daughter's death, but cannot change anything they do, listening to themselves justify actions that lead to their doom.
In one incarnation of the Doom Patrol, one of the men who goes by Negative Man can see a short distance into the future. He believes he can't change what he sees, and thus is understandably cynical.
The title character of the near-future gangster comic Skreemer had seen his whole future by the time he was in his teens, including who he would marry, who would betray him, and how he would die. This led to him taking outrageous risks (such as a home full of balconies with no railings, or walking through hails of gunfire). It also backfired in weird ways, such as when he told a loyal henchman that he knew he'd turn traitor — so the henchman did so, thinking it was what Skreemer wanted.
Lucifer's version of Yahweh suffers from this since he knows how everything will turn out since he created all the rules by which the universe works, started everything, and is everywhere. Lucifer's own attempts to defy Yaweh's foreknowledge were all planned for at the beginning of the universe. The second half of the series has Yahweh withdraw from the universe to try and create an outcome where he does not know every last detail. Even observing would render this moot. Surprisingly, this kind of works. He knew generally how things would turn out, but not specific details and is perhaps for the first time in his existence surprised by the ending.
Most notable literature example is probably the God Emperor Leto Atreides II, of the Dune novels. His plan, over three thousand years of his life is to influence human breeding so as to create a human whose actions cannot be predicted by precognitives or prescients. Bear in mind this is because Leto has calculated all possible futures and this course is the only way to prevent the extinction of humanityby ultimate prescient hunter-killer machines.
Before that, Leto's father Paul discovers the terrible truth of being an Oracle - the more a prophetic vision is fulfilled, the harder it is to avoid the rest of the vision, effectively being locked into it. It becomes worse after he becomes blind, and deals with the handicap by moving lock-step with his vision without any deviations. Eventually he realizes that the vision he had at first accepted wasn't such a great idea after all, and in the end he sacrifices his powers rather than see his vision out to its ultimate conclusion. It takes his son Leto II to work his way around this by merging his father's already in progress vision with several new ones played out for a few thousand years.
A slightly different take involves a weakness of the Spacing Guild. Because they use FTL travel, but don't have FTL sensors, navigators use prescience to choose a safe course. This leads them to use their other applications of prescience in the same way, choosing the safe course and not realizing others would choose the riskier way.
Averted in Slaughterhouse-Five. Although the Tralfamadorians see the past, present, and future as one, without any possibility of changing the future—and Billy Pilgrim, Unstuck In Time, comes to see time this way too—they accept it with equanimity.
Timequake, also a Kurt Vonnegut novel, plays it straight, though. The world had a kind of existential crisis and skips back to ten years ago. Everyone has to replay the last ten years, doing everything exactly the same as they did last time round but aware of what's going to happen.
Evanna the witch from The Saga of Darren Shan has this, and has taken a neutral stand on most things. Though, when she realizes that her father Des Tiny has fiddled with time and space to use his 2 sons to essentially cause a dystopian apocalypse, she realizes that maybe fate isn't totally set in stone.
The Clayr in the Old Kingdom series, by Garth Nix, like it when things go this way. They initiate new girls into their ranks because they had a vision showing that girl in the initiation ceremony. However, if the future becomes more and more difficult to see, that means more and more things are likely to go wrong... or that there may not be a future.
Atium in the Mistborn books is treated as the ultimate weapon, since it allows the user to see a few moments into the future and thus predict their foe's actions, but Vin manages to use this trope to defeat an atium-burner with a carefully-timed feint.
There is a story by Francis Carsac, in which the main character travels to a planet whose native population is slowly dying off from apathy. Nobody can figure out why. He eventually meets with another human who reveals that there is a hidden device that captures anyone who comes near and shows them their future in its entirety before letting them go. Worse, the natives consider it a rite of passage, so all of them go on a pilgrimage to the device. The man also reveals that he is supposed to die the same day. He is accidentally shot minutes later. The protagonist travels to the device and, predictably, is shown his own future. However, the device is almost out of power, so the vision is soon all but forgotten. He still remembers the name of his future homeworld, the death of his lion companion, and he death of the woman he loves. Even knowing the truth, he still goes to that planet, where all these events still happen (in another novel). The device turns out to be planted by Abusive Precursors who were about to die out, and were determined to allow no other race to take their place. (That's what they did to the less advanced planets; the more advanced ones were nuked outright.)
This is the reason that Good Omens' Anathema Device destroyed the book of prophecies left to her by her ancestor at the end of the book.
Though admittedly, knowing Agnes Nutter, the book was probably blank (or addressed to whoever ends up reading it).
Death from the Discworld series remembers everything. Everything that has happened or will happen.
Yet he doesn't have a clue when Rincewind is going to die?
He doesn't even know what Rincewind is anymore. He's had so much happen to him.
Or the order doesn't make any difference to him, and he's annoyed at Rincewind for all the future appointments he's missed as well as the current one and the past ones, because he remembers that at one of the appointed times he _does_ die but isn't 100% on which one it was so he has to show up to the others anyhow. I imagine that would kind of suck for an otherwise infinitely efficient and 100% effective force of nature.
It's mentioned that entities like gods and demons are technically timeless, but in practice live from day to day because it's so confusing otherwise. Death may do this as well, though to a lesser degree.
Though we never meet him, a central character in one of the Callahan's Crosstime Saloon stories, 'Fivesight,' has this in spades. He can see the future, but only the bad things, and he can do nothing to stop them from happening. Not the gruesome death of his lover's son, not their breakup, and not his own death at the hands of the dumb kid she'd been planning to cheat on him with...
Strangely averted by Artos in the Emberverse novels. After receiving the Sword of the Lady, he has clear and specific visions of the future seemingly at will, and there's no indication that they're anything less than 100% accurate and reliable. It never seems to get him down, though.
In the Fringe episode "The Plateau," a man is shown deliberately setting a pen on a mailbox, which serves as the catalyst for a chain of events resulting in catastrophe. It later turns out the man was the subject of an experiment that increased his cognitive abilities, allowing him to instantaneously calculate variables at a geometric rate, and resulting in his being able to both predict the future and also control it via chain reaction. Unfortunately, his mental speed eventually surpasses his ability to communicate with anything other than a supercomputer.
Played with in an episode of Old Harry's Game, where God is feeling depressed because everything is so predictable. He only snaps out of it once the Professor points out that God didn't know he was going to get depressed.
Entertainingly, his character is sometimes written as being so bored with how easy it is to predict the future that he complicates things arbitrarily just so it isn't anymore, making him the only chaos god who wants literal chaos more than some lower human desire.
Inspired by Emperor Leto in Dune, the Emperor of Mankind was also able to see the future. He was also immortal (to the tune of over thirty-seven thousand years old) so his plans could afford to be very long-term. Around the time of the Horus Heresy, however, his precognitive abilities were starting to become unreliable, even outright fading, to the point he didn't realize Horus' betrayal was imminent, nor that he was taking half the Space Marine Legions with him. Turns out, as you should know, this is probably due to his being nearly killed at the pinnacle of the Imperium-splitting civil war.
Every spanner in Continuum is subject to this, because their model of time travel says You Can't Fight Fate (though Narcissists disagree). Some try to avoid learning any more about their Yet than they have to.
Odin was cursed with this in Scion: every time he uses the power of Prophecy in order to attempt to avert Ragnarok, another piece of the future leading to it will be placed in stone. The curse was designed to stop him from abusing prophecy so much; at this point, the god who put the curse on him is in a total panic, because he didn't think Odin would ignore it the way he did, and now he wants to stop Ragnarok as well...
Exalted: Theoretically, the Maidens know everything that pertains to Creation, up to and including its ultimate end. But if they actually do, they aren't telling anyone, which only reinforces their air of mystery.
Fateweavers in Kingdoms of Amalur: Reckoning don't actually weave Fate as their title might suggest. They can only see a person's fate, which cannot be changed. The first Fateweaver you meet, Argath, was originally a famed adventurer and hero who thought becoming a Fateweaver was an honor. Then he read his own Fate and saw his own inescapable death: as the main ingredient of an ettin's stewpot. He started drinking pretty heavily after that.
The Master AI 'Oracle' from S.S.D.D is very close to this, engineering chaotic and unlikely events solely so he can observe the unpredictable outcome... rather than being caused by boredom, however, it's part of his basic programming: To observe matters in order to sharpen his own ability to predict future events. He just concluded that to improve his abilities further, he needed more chaotic and unusual events... and set about creating them.
In El Goonish Shive, this appears to be the main motivation of the shape-shifting Immortal entity dubbed 'Chaos' - she(?) hates predictability and influences events only to make them more chaotic and unpredictable. She helped the good-guys on several occasions, simply because she knew they'd lose otherwise - and she refuses to help the bad-or-not guy escape from his prison, since the only thing she really cares about is NOT knowing when, and if, he'll be able to escape. She only provides occasional hints, to keep him from giving up ('cuz that would be boring...)
She broke this rule of hers recently, but that was as part of her Berserk Button. FYI: Don't fuck with her son. It will end...badly.
Sarda of 8-Bit Theater often complained about the conversations he has with people because he already knew how they've turned out, and they were boring then. (Plus, having several billion years to muse them over probably hasn't done well by his sanity)
Aradia Megido from Homestuck has this in spades, thanks to her communion with the dead and later time powers. She is convinced they are all doomed and nothing they do can change this. She at one point considers killing Karkat just to create a divergent timeline that won't save them either. (Karkat is not amused.)
Played with in Girl Genius, from Othar's Twitter account. A girl from Paris volunteered for an experiment, but was basically stuck in mental time travel. For everyone outside, it was maybe an hour, but for her and the others inside the experiment, it was a thousand years. During that time, the girl predicted every event that would happen if she tried a heist, and was correct, until Othar got massively drunk.
Juno from Atomic Laundromat. She takes up working in the laundromat because it will be the site of something she cannot foresee.
American Dragon Jake Long gives us the Oracle Twins. One of them always sees bad futures, and has become so used to hearing bad news that everything makes her bright and perky. She is not an example of this trope. The other sister, however, only sees good futures, and in the spirit of this trope acts unenthusiastic all the time due to having all of the surprises taken out of life.
The protagonist of All Dogs Go to Heaven discovers a book in which all his future actions are written, and learns that in heaven, there are absolutely no surprises. The book didn't predict that he would flee heaven because of this.