Naruto should be the Master of Selective Obliviousness. He refuses to acknowledge that Sasuke has become a sadistic avenger bent on destroying their home village, despite the fact he KNOWS Sasuke has allied to Akatsuki and tried to kill him twice. While Your Mileage May Vary, Naruto is obliviously choosing not to accept the truth and the possibility of killing Sasuke. And if you consider just how much he meddles in other people's dark pasts and feelings, he's really unwilling to accept any other truth or way than his own.
It's not that he choose to ignore anything, it's just that killing Sasuke is simply NOT an option for him.
How he didn't realize Hinata had strong feelings for him, something many of the other ninja's were easily able to figure out.
Shikamaru thrives on this. He's got three girls showing feelings for him at once, especially Shiho, but he refuses to say anything to any of them, even Temari, who he personally likes. But this is for good reason: it's because his own mother goes off on his father at the drop of a hat.
In Ranma ½, the bombastic Tatewaki "Blue Thunder" Kuno refuses to believe that the hated Ranma Saotome and his beloved "Pigtailed Girl" are one and the same, even when Ranma changes right in his arms. After a while, one wonders if he isn't fully aware and just forcing himself not to think about it. His sister has a similar ailment, but she isn't confronted with the evidence quite as often (and in the anime, never) and actually tried to figure out what happened before getting sidetracked. Kuno might also be purposely ignoring all of the blatant evidence that neither of his "love interests" actually even likes him, let alone lusts after him... although this may be less Selective Obliviousness and more a cocktail of Casanova Wannabe grade lechery (Kuno is debateably a Handsome Lech) and whopping ego.
Akane Tendo is often accused of this regarding the fact that her pet pig is actually the cursed form of one of Ranma's rivals for her affections.
Hell, Akane Tendo practically lives this trope in both canons. It's got to be the biggest problem she brings to the relationship, even worse than her insecurity. That's not to say that Ranma doesn't contribute his own flaws, faults and problems, but when she's been shown to consciously ignore Ranma's attempts to explain how a situation wasn't what it looked like, to the extent that the manga version of Akane ignored Ranma's outright telling her why he was trying to grope Hinako, coupled with showing her the pressure point chart he was using, in order to support her own belief that it's because Ranma is an uncontrollable lecher... well...
To be fair to Akane, some of the situations really do look that bad (naked with Shampoo in the furo in a very suggestive pose for example) and in regards to Hinako, he was practially attacking her several times in her introduction arc, very much coming off like a pervert by grabbing her breasts, and without any explanation, it's doubtful that anyone would believe him.
In the anime canon, this flaw is actually the explicit reason why Akane is a Lethal Chef; she refuses to follow the recipe and adds extra ingredients that she ''believes'' will make it even better (and then adds the wrong wrong ingredients, due to not looking at what she's grabbing), and refuses to admit her cooking habits are why nobody will ever eat her cooking unless forced. In one episode, she spends the entire night trying to make edible cookies and continues to repeat the same mistakes over and over even though each and every batch turns out terrible. When Ranma finally allows himself to be guilted into eating her latest batch, and promptly takes to his room with severe stomach pains, Akane idly declares that the recipe must have been faulty.
Kasumi Tendo calls people who are actively trying to murder Ranma his "friends". Often Flanderized in Fan Fic into one of her defining traits.
Granted, considering Ranma's training tactics and his talent for annoying people, most of the people who look like they're trying to murder Ranma actually ARE his friends.
Mousse could be called Selectively Oblivious in regards to Shampoo. He refuses to admit that the girl he's been chasing since they were three has never shown any sign of reciprocated interest, at best ignoring him and more commonly hitting him whenever he made one of his "romantic" gestures/speeches. By the late manga, she's perfectly willing to let him die just to be rid of him. Instead, Mousse blames her lack of interest on her (willingly given and clearly backed by genuine emotion, at least in the anime) engagement to Ranma and frequently assaults the Japanese boy, accusing him of seducing Shampoo or otherwise keeping her away from Mousse.
One can also argue that Utena starts indulging in this after episode 31.
In Cromartie High School, no one (except Kamiyama, Hayashida, and the Doctor that preformed the school physicals) seems to notice that Mechazawa is, in fact, a robot.
The same for the student gorilla.
Kyon of Suzumiya Haruhi very deliberately ignores any hinting that the Chessgame of Life may have a King (who decides the game) as well as a Queen (who has the power in the game); he refuses to acknowledge Tachibana flat out telling him that he has the power to transfer Haruhi's power as well as Tsuruya's telling him that he and his friends really need to work on their Masquerade better.
And then there's just his ignoring Haruhi's feelings for him; over which she's willing to rewrite the whole of reality over. Even Itsuki is starting to get annoyed.
And then there's the fans, but that's a different story.
Souichi of the Boys' Love Genre manga The Tyrant Falls In Love doesn't seem to realize that he's making an awful lot of exceptions to his homophobia in regards to his gay companion Morinaga, not even after he says outright that he doesn't want Morinaga to leave him and that he can have sex with Morinaga only. That must be one hell of a balancing act between "I hate hate homos!" and "I can't let Morinaga leave my side, even if he likes me that way!" in Souichi's mind.
Nearly the entire cast of Hayate the Combat Butler has this about one subject or another (Sakuya, for example, believes her destiny is to become Japan's greatest comedienne, with Nagi as her partner).
Ouran High School Host Club: Tamaki persistently interprets his attraction to Haruhi as paternal affection; hilarity, naturally, frequently ensues out of the dissonance. Aside from Haruhi herself, no one else is fooled, and in recent volumes the other members of the Host Club speculate that Tamaki subconsciously refuses to acknowledge his feelings for Haruhi because he doesn't want anything to break up the surrogate family he's created in the Host Club the way his parents' love caused his own family to be broken up.
Penguin Revolution: It takes Ayaori six manga volumes of rooming together and, finally, actually seeing Yukari naked (with his contacts in, for a change) before he realizes that Yukari is a girl pretending to be a boy instead of a boy pretending to be a girl. Sure, he's Blind Without 'Em, but Yukari pretty much stops trying to keep the act up around him before the first volume is over.
In Detective Conan Ran has had suspicions about "Conan"'s identity, but not nearly as often as she should have, all things considered. (In one instance, Conan was terribly ill; he reverted to his normal appearance while nobody was watching him thanks to a drink he had been given by Heiji, then solved the mystery. He had a conversation with Ran, while obviously still very sick, then fell down the stairs and vanished in a puff of smoke. She heard Shinichi scream from nearby, and when she investigated, she found Conan instead. And somehow, she didn't figure it out.
Well, one could argue that she is satisfied for a while when there's a proper explanation. And she does try to trick him more than once. It seems that she kind-of accepted it as a fact by now, but she's waiting for Conan to tell her.
What about Heiji? He actually labelled his jealousy, when Kazuha flirted with a magician, as a 'leader's concern' for his follower....!
There was a Fan Fic take on this which suggested that Ran is, in fact, hoping she's wrong because she's Genre Savvy enough to have realized some of the implications of what she had been able to figure out, and would like to avoid going farther.
Satou's very much aware of Takagi's affection for her at least relatively early on, and she definitely reciprocates it. What she isn't aware of is how much nearly every other male detective in her department is crushing on her (well, except for Shiratori, but that was only because she got stuck in an omiai with him), to the point where she never seems really aware why the Absolute Defense Line keeps making things difficult for the hapless Takagi. She doesn't even realize that any ring on her left ring finger will typically symbolize engagement! On the other hand, considering that the last officer she was attracted to died at a mad bomber's hands...er, explosives...she may just be subconsciously tuning out anything that could lead her into that sort of devastation again. Takagi's genuine love for her is the only thing capable of getting through that membrane.
Misa in Death Note constantly professes to be talented when it comes to romance (and might well be), but constantly refuses to see that her beloved Light actually hates her. Admittedly, he acts otherwise fairly well, but not all the time, resulting in several Kick the Dog moments.
It's hard to say he outright hates her, it's more easy to say he's just using her, and she'll accept that. She doesn't realize however he's evil to some extent and not the Knight in Shining Armor she thinks he is, and she doesn't think he's capable of killing Rem. If he'd hate her, he'd just dispose of her after killing her Shinigami, but instead gives her the "choice" (more like order) to give up her note for the good of humanity. That's more than the chance he gave any other character close to knowing his secret, including "The voice of Kira" chick or the entire Kira investigating team.
In Axis Powers Hetalia, England doesn't seem to comprehend what colonial America meant by "Go to hell, England". Even in the present, he thinks of how cute of a kid America was.
To be fair, that was a very early strip and it seems to have been retconned since then. All the later strips show the relationship between England and little America as genuinely warm and fluffy, with little America pretending to enjoy England's cooking even though it's horrible, being happy to receive presents from England, and crying when England goes home.
Spain actually has this moreso than England, especially in the strip where he proposes to Romano. He merely asked for three meals a day without the slightest hinting to either option, but Spain automatically takes it as rejection.
America also fits in this, as Word Of God states that he "refuses to read the atmopshere". In other words, he can literally choose whether to remain oblivious to an event or finally pay attention to it.
Russia seems to think that other nations actually want to live with him. When one of them rebels and he does have to face the fact that they all hate him except for Belarus, he doesn't seem to have a clue why.
Sousuke from Full Metal Panic!. In the beginning, it looked more like he sincerely never notices when characters are in love with him. However, as the series goes on, it starts becoming more and more obvious (as his suitors become more and more direct) that he's actively turning up his obliviousness. This is no doubt due to his atypical upbringing, he probably has no idea HOW to react to such affection. His relationship with Tessa comes to mind, in particular. Numerous times, she makes incredibly aggressive advances on him, which he actually notices enough to feel nervous and scared. However, when people are later referring to her feelings for him, he's shown to react in a very oblivious manner, many times completely dismissing it.
Yurika in Martian Successor Nadesico tends to do this, insisting that Akito is head-over-heels in love with her, even though he's never shown any signs of it and tends to get pretty annoyed when she tries to get close to him. But it's possible that her obliviousness is all part of a master plan to make Akito fall in love with her. if so, it works.
This is actually a pretty strong plot point in Umineko no Naku Koro ni. Battler refuses to believe that a witch murdered everyone. Straightforward enough. However, he also refuses to believe that any of the eighteen people trapped on the island murdered everyone. Not only does he refuse to believe it, he actively rules out the possibility based on the fact that he doesn't want that to be the outcome, even when he acknowledges that the evidence points in that direction. Can you say "cognitive dissonance"?
This being Umineko, the truth of what's going is a bit more... complicated.
In Monster, Eva manages to overlook the fact that she had mistreated Tenma in the worst way - and when he tells her, nine years after she had broken off their engagement, that he is flattered but uninterested in reconciling, she chooses to turn a deaf ear and threaten him with telling the police that he had killed her father should he really decide to continue his life without her.
In Moyashimon, Aoi Mutou used to work hard at part-time jobs so she and her boyfriend could afford a place together. But one day, she arrived at his apartment only to find he had moved out, taken the money they had saved, and left a note saying he had found someone else. Mutou preferred to believe that he had been abducted by aliens, which is how she fell in with the agricultural university's UFO Club. Any attempts to bring up the obvious truth simply drive her to drink.
Upon learning that his daughter, Nagisais pregnant, Akio is torn between denial ("A stork brought it, right?"), joy at becoming a grandfather and wanting to strangle Tomoya for getting her pregnant. He does eventually (grudgingly) accept it. This is a rather extreme case, as Nagisa and Tomoya have been married for several months at that point.
Yamamoto Takeshi is the poster boy for this trope. He has seen talking infants wield guns, come very close to dying at least three times, traveled forward in time to stop an Omnicidal Maniac from destroying the world, and still thinks the mafia is an role playing game Tsuna and Gokudera cooked up. After being specifically told this isn't a game multiple times.
He takes game seriously though, not selective obliviousness in his case... he is just plain oblivious and idiotic. He definitely no longer think this whole mafia business a game once they transported to future, maybe before that he already was depend on your opinion how serious he was in battle. Hard to say since he smiled in 80% of his fights...
Asuka from Neon Genesis Evangelion does it as part of her Belligerent Sexual Tension with Shinji: while she never misses an opportunity to berate his perceived weaknesses and constantly calls him an idiot, pervert, etc., whenever he demonstrates evidence to the contrary, she makes a pointed effort to ignore it due to her severe intimacy issues. This becomes even stronger as the series goes on, eventually contributing to her mental breakdown when she realizes it's not working anymore.
Ikuto in Nagasarete Airantou is this to anything supernatural, dismissing it as his imagination or putting it into logical reason, despite living on a daily basis with talking animals and a kappa.
In Skip Beat!, Kyouka is completely oblivious to the fact that Ren is in love with her, even after his assistant blatantly told her.
Comicbooks
Can be seen in Western depictions of a Superhero with a secret identity, attempting to tell it to the loved one. (Example: Spider-Man's Aunt May.) One Superman story has Lois admonishing the Man of Steel for "that creepy Clark Kent impersonation." (Indeed, one might make a claim that the whole Superman mythos embodies this trope, as it would seem painfully obvious that Superman is just Clark Kent without glasses.)
J. Jonah Jameson generally frowns upon "costumed vigilantes", considering them usurpers of law and order. But he is willing to give the devil his due when it comes to true acts of heroism and is considerably lighter on those he feels have "paid their due" - like Captain America. Of course, there is a big Spider-Man-shaped blind spot in this P.O.V. - which, Depending on the Writer, can range in severity from Running Gag (Robbie Robertson constantly having to talk Jonah down from some of his more libelous headlines and editorials) to outright insanity (the newly-elected mayor of NYC Jameson gleefully watching a S.W.A.T. team open fire on Spidey without provocation.)
It's implied that, if Commissioner Gordon wanted to, he could figure out Batman's identity, but he deliberately chooses not to, and has in fact refused to look when Batman offered to reveal who he really was.
It's painfully obvious that Doctor Doom, being a supergenius and all, should be able to realize that Reed Richards had crap-all to do with the malfunction that caused Doom's experiment to blow up in Doom's face, and was only trying to explain to Doom that the experiment was flawed. However, Doom apparently can't stand the idea of Reed being smarter than him, so he steadfastly refuses to see reason and continues to try to destroy Reed's life in "revenge". It's hinted he does know this full well deep down though, as whenever Reed calls him out on this bullshit, he tends to fly into a homicidal rage, and at least once started beating Reed into a bloody pulp while screaming at him to admit he sabotaged the experiment "or else!"
Also, Loki often claims things like "everyone hated me" which may or may not be true. While most of Asgard does indeed dislike him, Thor himself foten references that he and Loki were happy together as children, and Loki just seems to block that time out so his Freudian Excuse is more credible.
Now he does know, since many people of Asgard were nice enough to point it out for him that his scheme led to The Sentrybringing Asgard crashing down. However, they are also unwilling to tell him almost anyuthing else (like who people are, what is happening at the moment, ect), since they still want to off him the second they think Thor won't care. The only exceptions so far seem to be the Warriors Three, who seem to do so very grudgingly (unless the story is funny or makes who Loki used to be look bad).
Fan Fiction
Kyon's mother in Kyon: Big Damn Hero refuses to acknowledge that Kyon had to get into a fight because of Tsuruya when she is told that Kyon had to replace Tsuruya's bodyguard, and instead decides to be full Shipper on Deck between them. And that was after scolding him for getting info fights at school (which happened because of Tsuruya too).
Film
Mars Attacks!!. Art Land is so intent about selling the investors on building his casino that he ignores the all out alien attack going on outside.
A creepy example in Shutter Island. An asylum inmate subconsciously created an elaborate illusion of residing in her neighborhood, and treated other patients and staff as neighbors or delivery men, flatly refused to admit that she's been committed for murdering her children. Then the unfolding story reveals that the protagonist suffers from that very delusion and that he created a far more elaborate illusion that placed him in the shoes of a federal marshall investigating the escape of the aforementioned inmate from the asylum and secretly searching for another inmate that killed his wife. In fact, the nonexistent escaped inmate is his wife, that murdered their children and thus drove him insane and the nonexistent killer is himself.
In Some Like It Hot, Jack Lemmon, masquerading as "Daphne", gets a marriage proposal from Osgood, an elderly millionaire. Daphne tries to talk him out of it:
Daphne: Well ... in the first place, I'm not a natural blonde.
Osgood: Doesn't matter.
Daphne: I smoke! I smoke all the time!
Osgood: I don't care.
Daphne: I have a terrible past! For three years now, I've been living with a saxophone player!
Osgood: I forgive you.
Daphne: (tearfully) I can never have children.
Osgood: We can adopt some.
Daphne: You don't understand, Osgood ... (ripping off wig) I'm a man!
Osgood: Well, nobody's perfect.
This is what the title of An Inconvenient Truth refers to (specifically, being unwilling to observe something because your job depends on you not observing it).
Literature
In The Hitchhiker's Guide To The Galaxy (at least the novels), Zaphod is literally selectively aware of his own motives, due to having both of his brains surgically altered so that certain thoughts wouldn't be detectable by the brain scans he needed to undergo in order to become President of the Galaxy.
This is also in the movie. It's more of a Hand Wave of Zaphod's two heads because they don't go into specifics.
Mostly Harmless features a species of bird that is oblivious to every strange thing that happens, like ignoring a fiery spaceship crash. However, they are always shocked by perfectly mundane things. For example, "...And sunrise always took them completely by surprise."
Clifford manages to be shocked when he finally learns that his wife has been having an affair with another man in Lady Chatterley's Lover. His maid recognizes that he subconsciously knew about his wife's infidelity from the start, but just didn't have the courage to face it.
In Discworld, Twoflower is besotted with the idea of Rincewind as a Great Wizzard (sic), and refuses to realize that he's completely incapable of doing magic. This is far more prominent in Interesting Times, though, as he does seem to exhibit something approaching realization in The Colour of Magic.
Also in the same series, the Duck Man refuses to realize that he has a duck on his head, regardless of how many people tell him so in no uncertain terms. This is more Rule of Funny, though.
Lord Rust is also well known for, as the author puts it, "Erasing unwelcome sights and sounds from his personal universe". This causes problems for him when people like Detritus and the Dean of Unseen University are apparently too large to erase, and hilarity when Vimes takes advantage of it to swear at him without him noticing.
In The Secret History, Julian knows every important part of the plot, except for the crucial fact that five of his students killed the sixth one. He wants to believe the best of them, but really, it's not a huge leap to make...
Early on in Quills Window, Courtney Thane's mother writes to him that she genuinely has no idea why his father cut him out of the will right before he died, and Courtney's sentiment seems to be the same. When we find out the reason for this later in the book, it becomes quite obvious that if either of them had engaged in serious self-reflection they would know the reason behind the father's I Have No Son moment.
This is the cornerstone of Doublethink. Bonus points for the requirement that obliviousness must not only be selective but also instantly switchable — you must completely and sincerely forget whatever you vehemently believed in a moment ago and, if necessary, switch back the next moment — and recursive — you must forget that you've just forgotten something, forget having forgotten that, et cetera.
The mind should develop a blind spot whenever a dangerous thought presented itself. The process should be automatic, instinctive. Crimestop, they called it in Newspeak.
He set to work to exercise himself in crimestop. He presented himself with propositions — 'the Party says the earth is flat', 'the party says that ice is heavier than water' — and trained himself in not seeing or not understanding the arguments that contradicted them.
Crimestop means the faculty of stopping short, as though by instinct, at the threshold of any dangerous thought. It includes the power of not grasping analogies, of failing to perceive logical errors, of misunderstanding the simplest arguments if they are inimical to Ingsoc, and of being bored or repelled by any train of thought which is capable of leading in a heretical direction. Crimestop, in short, means protective stupidity.
Johnnie Rico in Starship Troopers. While he tries hard to paint himself as "just another ape", reading between the lines shows he's pegged as leadership material almost from the start.
A short story (author, title forgotten) from the 1950s or 60s has a space traveler land on a planet. He encounters a village with two populations, where persons of one population are oblivious to anyone in the other. They dress very differently, so the main character can distinguish between the two. Representatives of both populations see him, because his dress is ambiguous. There is at least one hint that the obliviousness is pretended: Children sometimes interact with children from the opposite population. Parents often find an excuse to spank those children. The main character resolves the issue by turning on a ray that causes everyone's clothes to melt.
The Ministry of Magic in Harry Potter choose not to believe that Voldemort is back in Harry Potter and the Order of the Phoenix despite the overwhelming evidence. They lead the public to believe that all is well and constantly berate Harry and Dumbledore as liars. It's explained that they have a contrived denial caused from how horrible Voldemort's previous reign of terror was. Despite this explanation, many fans interpreted them as Too Dumb to Live.
In Book 4 it's briefly mentioned that Petunia, who could spot the tiniest imperfections that could be used for gossip fodder, refused to see that Dudley's obesity had reached dangerous levels (in the book he's compared to a young killer whale). She only sees reason after the Dudley's school nurse sends her a letter about it since the school doesn't stock uniforms in Dudley's size.
Given that by the next book he has lost all the extra weight and is an accomplished boxer, they must have had a fairly limited selection (or he had an inhuman metabolism).
For the whole year, Dudley had been eating what essentially amounted to a couple of grapefruit a day, and with the exercise that came from boxing, he would've lost enough weight to make an anorexic proud.
In the Jin Yong novel Smiling Proud Wanderer Linghu Chong, despite usually being quite perceptive and it becoming glaringly obvious, cannot grasp that his master is a scheming coward who doesn't care one bit for either Linghu Chong or any other of his pupil.
The residents of Valdemar have a magically-induced blind spot when it comes to the existence of magic and the true nature of their Companions. For example, the scholars of Valdemar insist that the ballad of Kerowyn's ride, an account of more or less contemporary events, is meant to be interpreted metaphorically even after the real Kerowyn shows up in Valdemar and becomes one of the Queen's best-known advisors.
Tobias: You know, Mother Lucille, there's a psychological concept known as 'denial' that I think you're evincing. It's when a thought is so hateful that the mind literally rejects it. Lucille: You are a worse psychiatrist than you are a son-in-law, and you will never get work as an actor because you have no talent. Tobias: Well, if she's not going to say anything, I certainly can't help her.
Rachel of Friends is in constant denial about her true feelings for Ross when she's not with him. On the day before Ross's wedding to Emily, she somehow finally figures it out: "Sure, I like Ross, but feelings are really complicated... maybe I am sexually attracted to him, but I do love him... oh my God." When she demands of Phoebe on why she didn't tell her about her own feelings before, Phoebe replies, "Well, it's so obvious to everybody. It's like saying, 'Gosh Monica, you sure like to clean.'"
Chandler asks for no strippers at his bachelor party, and after he leaves Joey immediately asks what kind of strippers they should get. Ross reminds him what just happened, and he replies "Huh. I chose not to hear that."
The Colbert Report: Stephen Colbert insists that he is completely straight. Evidence to the contrary is dismissed with convoluted excuses when possible, ignored when not (as with the diagram of his brain in which one area was labeled "Repressed Homosexual Urges").
Gul Dukat on Star Trek: Deep Space Nine. His imagined friendship with Captain Sisko escalates to ridiculous levels throughout the series, to the point where he chides Sisko for being so obtuse about his feelings while on the opposite sides of a battle line or in the middle of a no-holds-barred hand-to-hand fight. In fact, you could probably form a whole section on all the things Dukat pointedly ignores. (Although, from what little has been revealed of the Cardassians, that may be how they express friendship, or he may be doing it just to annoy Sisko.)
In Strangers with Candy, the homophobic Principal Blackman is the only one who doesn't know that Chuck and Geoffrey are lovers. At one point he catches them in the school basement and happily accepts the explanation that Chuck is showing Geoffrey the furnace system, even though Geoffrey has his trousers round his ankles.
In Lie to Me, Gillian readily accepts her husband's feeble excuses about having to work late, even though her job is based around the ability to tell instantly when someone is lying.
On Angel Wesley managed to be totally oblivious to Fred's feelings for him in Season Five. This came to a head in an episode when he lectured Angel about the latter's failure to notice Nina's interest, while himself remaining totally unaware of Fred's. She eventually resorted to a Forceful Kiss to get the message across.
In Season Three, Cordelia was this way about Angel's feelings for her. Fred seemed to be likewise re: Wesley's feelings for her, until Gunn later casually mentioned that she knew about them.
Played with in Hannah Montana where Miley mentions that she's kissed, and quickly backpedals prompting Robbie Ray to say "I love our relationship, you pretend you don't kiss boys, and I pretend I believe you"
In The Mighty Boosh, whenever Vince says or does something suggestive towards Howard (which is quite often) Howard will either walk away or awkwardly change the subject, totally ignoring it
The Doctor about Martha's feelings for him during Season Twenty-Nine. "It's right in front of me and I can't see it" indeed.
Martha and Captain Jack Harkness both, apparently:
The Doctor: Oh! I know what it's like. It's like when you fancy someone and they don't even know you exist. That's what it's like. (runs off)
Martha:(stares despairingly after him)
Captain Jack: You too, huh?
Guy of Gisborne from Robin Hood chooses to ignore the mounting evidence that Marian is in cahoots with Robin Hood. By the final episodes of season two, he's in complete denial.
A very common theme in Hoarders, where people don't seem to notice they're living in squalor. One episode featured a woman who had a lot of dolls. At one point she picks up a small doll that's the size of a soda can and declares that it doesn't take up any space, completely ignoring the 8-foot-tall mountain of toys in front of her.
In Season 6 of Buffy the Vampire Slayer Xander witnesses some blatant clues that Buffy is having a secret affair with Spike (most notably Spike doing 'naked push-ups' on a day that Buffy's been turned invisible) and ignores all of them as the idea of Buffy lowering herself to have sex with an Evil Bloodsucking Fiend is unthinkable.
The beholders in D&D are like this by design. They have two brains. One is responsible for higher logic. The other hosts emotions and instincts, and is responsible for interpreting the data input from the senses. Thus, if something is against the beholder's beliefs, it will never get far enough to be considered on logical level. Too bad their genetic memory gives them the beliefs of rampant, murderous racists. The only reason they manage to survive at all with such a mindset is that their creator have also found it fitting to grant them innate massive firepower.
At Act I Scene IV, Cyrano fails to notice that the buffet-girl is a Smitten Teenage Girl with him. He is so convinced he cannot be loved, that Le Bret must point out to him this fact (see Oblivious to Love).
In Prototype soldiers will react at the display of the protagonist's Lovecraftian Superpowers or explicit hostility but super-fast runs, super-high jumps, running up a wall or falling from the sky and punching a crater in the pavement will be ignored.
Justified in a Fridge Brilliance manner because the protagonist can slaughter them without thinking about it, and most soldiers would rather keep on living.
And the game wouldn't be very fun if you couldn't move around without being attacked.
Role-players in City of Heroes (and presumably other games) almost require this trope for certain scenarios to take place. For example, there's certain to be more than one (or more than fifty) characters running around who all claim to be the same specific character from mythology (popular examples include Thor, the Devil, and even Santa Claus). If one accepted that all these characters' stories are true, even though they clearly contradict each other, they'd go insane.
Also tends to be a vital tactic in other areas of roleplay: text-based combat (rather than in-engine PVP) often times breaks down into "Bang bang! / OH I dodged! / No, I shot you / no you didn't!" levels of quarrels; Selective Obliviousness is oftentimes the only way to resolve a situation before ending up needing to get mods involved.
Visual Novels
Masayuki refuses to see the bad in people in A Profile or to distrust his friends. He simply won't notice such things.
Reiji actually does realize how Kyoko feels in Kara no Shoujo. He just thinks it wouldn't be right to start a relationship with her.
Shirou in Fate/stay night seems to have a slight awareness of Sakura's interest in him, but considering he's in denial about his own attraction to her, she's made nearly no progress in over a year and a half of trying.
Junichi in Da Capo is actually perfectly aware that Nemu likes him and has for years. He wasn't just completely dense. On the other hand, she's his adopted sister, which makes things kind of awkward, so he simply did his best not to think about it.
Webcomics
In 8-Bit Theater, Thief constantly denies the existence of dragons. Despite the Light Warrior's direct interaction with several of the mythic lizards, Thief maintains that dragons are extinct.
In El Goonish Shive, Melissa is so madly in love with Justin, she keeps asking him out even after it is revealed that he is gay. Justin, needless to say, finds this extremely irritating, especially since she is the one who (either directly or "indirectly") blew the secret.
In her case it might be worse than that: in a strip she even stated that "he's just going through a phase".
However, in a later strip (after Melissa started becoming a more prominent character), it's indicated that Melissa is fully aware that a romantic relationship with Justin is a lost cause, but can't seem to stop herself without a friend around to snap her out of it.
Earlier in the series (though chronologically after Justin was outed), Elliot pretended not to notice Sarah's feelings towards him, because he was afraid that a romantic relationship with her would destroy their friendship; he may have had Justin and Melissa's ruined friendship in mind, since he'd known Justin for some time at that point.
In Fans, club president Rikk is utterly oblivious to fellow member Rumy's painfully obvious attraction to him. When third member Katherine gets fed up with this and tries to inform him directly, he exhausts every other member in the club, Katherine included, as potentially having a crush on him. Not once does he even consider Rumy.
In Flipside, Blithe Spirit Maytag has a complete and utter lack of any sense of modesty. And an equally complete and utter lack of understanding it in other people. To the point where she's openly baffled when everyone else is upset when their carriage driver is caught using x-ray specs to peep through their clothes. Given the grasp of human nature she shows when she's in Manipulative Bitch mode, this is almost certainly self-justification for her own exhibitionist ways.
Van Von Hunter is sworn to destroy anything evil that he encounters. However, he "doesn't notice" that Ariana Rael, the Child Mage tagging along with him is ungodly evil. The fact that she could destroy him with a thought has nothing to do with why he's not picking a fight with her...
In Misfile, Doctor Upton can hardly have failed to have noticed that his "daughter" appears to have developed some rather severe identity problems, especially considering that it was shouted out at full volume at one point. Despite this, the issue is never raised.
Randy, the tame fox in Faux Pas, is so naive about sex that it's impossible to think this trope isn't going on. This alternately frustrates and amuses the wild vixen who wants to be his mate.
Web Original
In Red vs. Blue Reconstruction, Sarge is unable to understand that Grif is now the same rank as him. Grif actually suggests that he is physically incapable of comprehending that fact.
Western Animation
In King of the Hill, despite his rampant paranoia and suspicion of everyone and everything, Dale Gribble is completely unaware that his wife is having an affair, although it's obvious to everyone else — with the exceptions of Joseph, "his" son, and Peggy (who gets clue-by-four'd later on). Nobody has the heart to tell him about it.
That's because despite his paranoia, he trusts those closest to him — his friends, family, and neighbors — implicitly. And because of howhe'dreact if he ever found out two of his closest friends betrayed him. He's equally oblivious to his father's homosexuality for much the same reasons.
One episode reveals he thought John Redcorn was gay; he does eventually confront the fact that Joseph can't be his son, but comes up with a story involving aliens to explain how he really is.
Invader Zim has two cases: Zim, who refuses to acknowledge that his leaders would like nothing more than his swift and painful death, and Dib, who thinks that exposing Zim as an alien will change how his family and peers think of him, despite plenty of evidence to the contrary.
Panini from Chowder doesn't understand the meaning of the words "I'm not your boyfriend."
Mr. Herriman can spot the tiniest speck of dirt, but he couldn't tell a crudely made decoy of Eduardo from the real Eduardo.
On Total Drama World Tour, Cody. Courtney a bit too, though she was at least suspicious that Duncanwas cheating with Gwen behind her back; when Cody found out he seemed completely shocked, despite the fact that in-universe it's been a common theory they liked each other going back to season two.
