Usually, in modern stories, a character who's a sexist, racist, or something else of that kind is the bad guy. This is mostly due to the present day view that prejudice is generally bad.
Sometimes, either due to an Author on Board, Values Dissonance, Rule Of Cool or something else, a character can get away with opinions that are... controversial. If the excuse is well-done, it can work. If not, it seems like a Karma Houdini. Unless, of course, he is punished for it.
See: Bury Your Gays because it's disturbing how similarly these two often work. Also see Good Flaws, Bad Flaws for a more thorough analysis of "discrimination as a flaw".
Examples:
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Anime and Manga
Ranma ½: Ranma exhibits a surprisingly homophobic attitude in the storyline dealing with Tsubasa.
Akane also had a sexist attitude towards boys (though not men) in the first season.
Wufei from Gundam Wing in an early episode explains away an opponents weakness because "she's a woman". He then goes on to spare her life because "I don't kill weaklings or women" (thus equating women with weaklings). Eight episodes later another character (yes, a woman) helps pull his head out of his ass, and his Character Development gets him out of that mindset by the end of the series - but these epiphanies tend to get ignored by viewers. As for skilled female pilots, Noin can stand alongside the show's mains and do so while piloting an inferior mecha.
Athena in Hayate the Combat Butler, taught Hayate that a guy had to be able to support a girl financially before he could consider romance. When this is told to the reader, it's blatantly made clear by the other characters that it's wrong. And that's before the realization that most of the girls (including Athena herself) could sit on their hands for a day and make more money than a normal guy could in a lifetime, coupled with Hayate's eternal poverty makes it impossible for him to see that he has at least a dozen young women all but throwing themselves at him.
The Nations of Axis Powers Hetalia constantly make extremely offensive jokes and slurs against each other. The entire thing is generally Played for Laughs, owing to the fact that most of said Nations who do that sort of thing are just as hotheaded or stupid as the one they're insulting (also, the series pretty much runs on Refuge in Audacity).
Lance Blastoff from Frank Miller's Tales to Offend. It's probably intended as parody but, with Miller, it's sometimes hard to tell.
In a Runaways story arc where the group finds themselves in the 1800s, a number of the "talented" street urchins they stay with refer to the Asian-American Nico as "the oriental" (she corrects one person with "I'm Japanese, by way of Glendale"). When Klara sees Karolina being intimate with Xavin (who is in his/her usual body of a black human woman), she freaks out at how "wrong" it is and refers to Xavin as a "negress". She seems to get past it when they bring her to present times.
Justice Society of America member and golden age Green Lantern, Alan Scott (pre-2012 reboot), had admitted that he would never fully be able to accept homosexuality as normal.
A lot of monster movies have the girl falling in love with the biggest chauvinist in the cast. King Kong probably started it, but it's alive and well twenty years later in Them! and the MST3K-ified The Deadly Mantis.
James Bond, especially when played by Sean Connery. Seriously, he treats women as nothing more than sex objects. In Goldfinger alone he actually rapes two of them (first that one girl on the balcony who is helping someone cheat at gin rummy and then later on Pussy Galore) and everyone is okay with it, not to mention that whenever his girlfriends get killed horribly, he barely spends more than a few minutes grieving before he is in the arms of another in the very next scene, apparently having completely forgotten about the other girl he just confessed his love for. In any realistic setting he probably would have been court-martialled... several times, and he would be fired from the British secret service if it weren't for the fact that they apparently don't have any other agents remotely competent enough to do the job.
Think he's bad in the movies? Try reading Ian Flemming's original novels. He was far worse there.
Cpt. Stanley in The Proposition really does mean well, but he's certainly a man of his time in terms of his views on gender politics.
In Who Framed Roger Rabbit?, bigotry against toons seems sadly common, and even Eddie Valiant, the protagonist, shows signs of it initially (although it is somewhat justified in his case, seeing as his brother was murdered by a toon). There are still a few toons who he regards as friends at the beginning of the film, however, like Betty Boop.
The Mole in South Park: Bigger, Longer & Uncut is a character who helps the boys rescue Terrance and Phillip, but can barely go 30 seconds without saying something extremely blasphemous.
Although, given his background of having survived an abortion, his outright hatred of God makes some sense.
The truncated ending to Twilight Zone The Movie film segment "A Quality of Mercy" seems to suggest this, as Mr. Conner ends up shipped to off to his death in a concentration camp as punishment for simply being a bigot, with the Unfortunate Implications that bigotry not only should not be forgiven, but it cannot be forgiven. Of course, this message was not intended: Mr. Conner was going to be redeemed in the original ending after risking himself to save two young Vietnamese children, but a tragic freak accident on set forced the director to go with the much darker ending shown in the film.
In Gran Torino, the main character (played by Clint Eastwood) is a racist white veteran of the Korean War who has several disputes with his Hmong neighbors. Though he eventually warms up to them and they to him, he makes several politically incorrect jokes at the expense of Asians.
He's also shown to good-naturedly swap ethnic barbs with his white friends ("What's happening, ya greasy dago" "Not much, ya dumb Pollack"), suggesting his slurs aren't necessarily mean spirited. Racial sensitivity is just something he never learned.
Chinatown is set in the 1930s and Jake has a um... period authentic attitude toward minorities.
He also likes telling dirty jokes, usually unaware of women Right Behind Him.
Even the non-corrupt officers in L.A. Confidential are slightly racist towards African Americans.
He wasn't the protagonist, but the co-pilot in Snakes on a Plane was constantly on the edge of a sexual harassment lawsuit with the way he talked. After the pilot died, he locked himself in a cockpit full of snakes and kept the plane up until he died, making suggestive jokes to the flight attendants up to the end. To their credit, he was fairly good friends with the flight attendants, and it was mostly just friendly banter.
The titular character of Dirty Harrydefinitely qualifies:
Gonzales: There is one question, Inspector Callahan: Why do they call you "Dirty Harry"?
De Georgio: Ah that's one thing about our Harry, doesn't play any favorites! Harry hates everybody: Limeys, Micks, Hebes, Fat Dagos, Niggers, Honkies, Chinks, you name it.
The Dictator and Borat. Since Sacha Baron Cohen is involved, it's not surprising the protagonists are over-the-top racists, misogynists and antisemites.
In the original Lethal Weapon there are two lines of dialogue that imply that the character Martin Riggs (Played by Mel Gibson) is somewhat homophobic. Well, it was the 80s.
The Last Boy Scout (Also written by Black) uses the same line "What are you, a fag?", this time by the protagonist Joe Hallenbeck
In Con Air, the prison guard in charge of transporting the prisoners calls Pinball "the skinniest Negro I have ever seen".
Literature
Eddie Valiant from Who Censored Roger Rabbit? (the book that inspired the similarly-named film) starts out as a shameless fantastic racist, thinking of the Toons as second-class citizens incapable of behaving with dignity or even of feeling the same emotions as humans. Throughout the course of his adventures, however, he learns to chill out and treat everyone's needs equally, eventually understanding that though they're fundamentally different in many ways, Toons are people too. He never stops being a bitter Deadpan Snarker, though.
The Andalites, the "good guy" aliens from Animorphs, in addition to being generally arrogant and seeing themselves as better than other species, are also sexist (feeling female Andalites shouldn't become warriors) and hate Andalites with disabilities, which they call "vecols."
To be fair, it's a bit more nuanced than that: females aren't traditionally warriors, but they are scientists and artists in a society that subvertsKlingon Scientists Get No Respect, and one book shows that female military cadets are a recent innovation. Disabled Andalites are excluded from normal society, but apparently it's felt that this is for their own benefit (a belief that Ax eventually realizes is misguided).
The Hunters of Artemis from Percy Jackson and the Olympians all hate men and boys, but are willing to help them for the greater good.
Averted by Commander Vimes, but played straight by Sergeant Colon, and both are discussed in the same discussion. Fred Colon gets the "product of his time" excuse; he's somewhere in late middle age when he's introduced in Guards! Guards!, and upgrades to "elderly" sometime before Thud! He's known to think of dwarfs and trolls as "gritsuckers" and "rocks" (speciesist slurs, both), and is a little too eager to buy into anti-Klatchian propaganda in Jingo. Vimes, by comparison, comes off as a bit speciesist on the surface, but A) nonhumans under his command put up with it because they know he's got their back when they're in trouble and B) he doesn't much care for humans, either.
It can be summed up as "Sam Vimes only likes other coppers, his wife, their child, and their butler." (And it doesn't hurt that Willikins the butler is a member of the "Specials"—The Ankh-Morpork City Militia.)
In Stephen King's novel The Running Man, first published under the pseudonym of Richard Bachman, the main character is this. He uses the words "Negro" and "nigger," both of which mark him as out of place in 2025, an anachronism. Of course, you're still supposed to sympathize with him because he's trying to get onto one of the Network's sadistic game shows in order to make money so that his sick infant daughter can get decent medical care.
The Running Man is a dystopian future novel, though, and it's unclear where that timeline diverged from the real world. 'Negro' is more understandable when seen alongside other deliberately archaic terms and references like 'atomic' in place of 'nuclear;' also, Ben's only use of the word 'nigger' was part of the phrase 'house nigger,' which has a different meaning than just calling someone a nigger. A 'house Negro' is one who lives and works indoors alongside the master, in contrast to the 'field Negro' who works outdoors and has no chance at any of the comforts that the house Negro has. Thus, house Negroes are loyal to their master because, if sold, they stand a good chance of being field Negroes under the new master; they are presented as traitors and dupes who allowed themselves to be turned against their brothers in the field in exchange for literal table scraps. The Other Wiki, as always, has plenty more information on this.
Sisterhood series by Fern Michaels: Oh, man. Books like Weekend Warriors and Vendetta show that a number of the Vigilantes are very anti-Asian. Kathryn went into a rant at Yoko Akio about how she's using the fact that she's Asian and different as an excuse to be wishy-washy. Yoko is not wishy-washy. One of their targets is a man named John Chai, who they keep calling "Chinese boy". They don't call him anything worse than that, but the fact that the book he's in blatantly uses Yellow Peril to justify putting him in the role of the villain implies that the Vigilantes are very anti-Asian, despite the fact that one of their members is Asian herself! Later on, the Vigilantes pretty much indicate that they are Straw Feminists and misandristic, which male readers will not appreciate!
'Fat Ollie' Weeks from the 87th Precinct novels by Ed Mc Bain. Very much a Noble Bigot with a Badge, Ollie's multiple prejudices don't get in the way of him being very effective cop; possibly because he seems bigoted against all groups equally.
While he starts out in the story as a Designated Hero, Kyle Kingsley of Beastly makes a number of comments about objectifying women, and explicitly states at one point that he knows what to do to manipulate his girlfriend into being happy enough to have sex with him. This is contrasted to how he eventually views Lindsey, valuing her intelligence and personality and wanting a meaningful relationship with her, all of which show his growth as a person.
Remo and Chiun of The Destroyer regularly throw out sexist and racist comments and are called on it by other characters. Then again, the way their world is, they're not always wrong.
Kvothe from The Kingkiller Chronicle subconsciuously objectifies women. This becomes obvious when he likens women in general to music instruments to be played by him, acknowledges that women would consider that rude and sexist, and accuses them in advance to not understand his love of music - in his subconscious worldview, women actually are objects and thus can only rightfully feel insulted by comparisons to worthless objects, not by comparisons to valuable and beloved objects.
This illustrates the fact that it is impossible to completely separate oneself from one's culture. Kvothe's male enemies are usually much more explicitly sexist, and he disapproves of their behaviour, which makes him somewhat likeable in comparison.
Live Action TV
Perhaps the Ur example for television (at least in the US) is Archie Bunker from All in the Family. Racist, sexist, the whole nine yards. The only reason the show got away with it was because Archie was portrayed as an idiot for having these views.
The titular character of House says some pretty sexist things, but then he is pretty much an equal-opportunity insult-slinger. (Not that such a thing always stops complaints.)
Cuddy (evaluating House) Your attitude towards supervisory personnel is disrespectful, and a disturbingly large proportion of your comments are racist or sexist.
DCI Gene Hunt from Life On Mars and Ashes to Ashes is a particularly good example. (Heavily lampshade-hung in the Season 1 finale of A2A, when Alex tells Gene there's a sizeable percentage of otherwise intelligent twenty-first-century women who'd be perfectly happy to sleep with him.)
Gene Hunt: Now. Yesterday's shooting. The dealers are all so scared we're more likely to get Helen Keller to talk. The Paki in a coma's about as lively as Liberace's dick when he's looking at a naked woman, all in all this investigation's going at the speed of a spastic in a magnet factory.
Sam Tyler, shocked, drops the radio he is holding.
Gene Hunt: What?
Sam Tyler: Think you might have missed out the Jews.
The Todd in Scrubs constantly sexually harasses the female staff at Sacred Heart, and says many sexist and derogatory things....yet remains one of the most popular side characters, second only to the Almighty Janitor.
The Todd is loved not in spite of his sexism as per this trope, but due to it being taken to absurd and frightening levels. Plus later he starts going after men too. Why? Because he is THE TODD.
Arguably, Dr. Christian Troy from Nip/Tuck: pathologically oversexed, determinedly shallow, given to anything from sexual harassment on up to psychological warfare as seduction tactics (see, for example, the scene in the pilot where he strips his latest conquest naked, stands her in front of a full-length mirror, and uses a red lipstick to indicate flaws he finds surgically improvable), and an overwhelming fan favorite. Possibly because of the hotness, possibly because of the tragic backstory, possibly because he's the only major character who isn't an insufferable hypocrite.
Big Bad Ari from NCIS is constantly being paired off with members of the main cast- male and female- including the woman he shot in the head and all the people he's attempted to do so to. (Probably Gerald, too. Shiver.) He's also got a healthy streak of sexism to go with his sadism, dad issues and thrill seeking. A Magnificent Bastard, but maybe less than magnificent.
Also Gibbs. Ari killed one of his female agents precisely because Gibbs would be more upset about it than if he'd lost a male subordinate. He shows no respect for his female boss (unlike her male predecessor), and it's suggested that he has trouble taking orders from a woman.
Mike Franks, Gibbs' mentor, fits this trope even better. His sexist views are FAR more blatant. When he found out Jenny Shepard was the director of NCIS, he laughed at her since she was a woman.
Dennis Duffy on 30 Rock. He's a sexist, homophobic, racist lout who calls Liz "Dummy" and embarrasses her in public. Oh, and did we mention he happens to be an Internet predator? (Actually he was apparently later exonerated) Well, Liz sporadically dates him and some fans seem to like shipping them together. Witness a break-up speech he delivered:
"Dear Liz Lemon, Though other women have bigger boobs than you, no women has as big a heart and when I saw you getting ready to go out and get nailed by a bunch of guys last night, I knew for sure it was over between us and, for the first time since the '86 World Series, I cried. I cried like a big dumb homo. And if it were up to me, we'd be together forever, but there's this new thing called 'Women's Liberation' which gives you women the right to choose and you have chosen to abort me and that I must live with."
And Jack Donaghy on the same show. Only Alec Baldwin could get away with the line "I like a woman with ambition; it's like seeing a dog wearing clothes".
Liz herself has some racist tendencies, but continues to be loved.
He also has enough genuinely decent moments to keep him firmly in the Jerk with a Heart of Gold territory.
Barney: At one point, I'm pretty sure I sold a woman. I didn't speak the language, but I shook a guy's hand, he gave me the keys to a Mercedes, and I left her there.
Chief O'Brien on Star Trek: The Next Generation and Deep Space Nine was a (somewhat) Licensed Fantastic Racist against the alien Cardassians. In one of the few Next Generation episodes that gave him a prominent role, he explained his excuse for this — during a war with the Cardassians he had to kill another person for the first time (in self-defence), and hated himself for doing so. Of course he still got a lot of flak for his racism, especially in a much later episode of Deep Space Nine when he showed a lot of dislike for a young and innocent Cardassian child (though he got better over time). Nonetheless, he was generally a very likeable and sympathetic character.
Kira follows a similar, more dramatic character arc. Her absolute hatred of all military Cardassians was pretty justified, since she spent her entire life fighting against their horrifically brutal occupation of her planet. Over the course of the series, she came to accept that not all Cardassians are evil, and even began to sympathize with them when their planet is occupied.
To make this understandable, it should be noted that the Cardassians as a species are not very far from Always Chaotic Evil. Their regime is horrible, and most Cardassian characters are representatives of that regime in one way or another (though we do meet some genuinely noble ones...andGarak).
Commander Worf is openly racist toward Romulans, to the point that simply admitting that Romulans fought honorably in their failed Gunship Rescue is treated as legitimate character growth in Star Trek Nemesis.
Worf once refused to donate blood to a critically wounded Romulan, resulting in his death. He's also portrayed as quick to resort to violence (Though that's common for a Klingon) and slightly sexist in a "Women are delicate and need protection" sort of way.
A rare female reference from Doctor Who: In "The Family of Blood", love-interest Joan Redfern explains at length why Martha cannot possibly be a doctor. Martha's response may well constitute a Crowning Moment of Awesome. In her defence, Joan Redfern lives in 1913, when women practicing medicine as doctors in British society was a rarity and genuinely was thought to be impossible by many people, let alone black women doctors...
Lampshaded in "The Shakespeare Code", when Shakespeare becomes smitten with Martha. She is initially offended by him calling her an Ethiopian and such things, until she realizes that he's trying to compliment her. The Doctor comments on all of this with "It's political correctness gone mad!"
Douglas Reynholm in The IT Crowd plays this for laughs.
Buz Murdock of Route 66 is a Licensed Sexist, and made at least two cringe-inducing speeches about a woman's place as helper and subordinate to her man during the show's run. He's the lead character and portrayed sympathetically: the women agree more often than not, and see the "error" of their ways! His view of relations between the sexes is, arguably, a bit of Author Appeal.
A recurring character in Series 3 of That Mitchell and Webb Look is Captain Todger, a superhero with an outdated, Bernard Manning sense of humour, whose emblem is a crude drawing of a penis.
Mayor:"He'll never kneel, because he is our greatest hero, and has saved humanity countless times!"
General Drayfox: (An incredibly PC supervillain) "THEN WHERE IS HE?!"
Mayor:"Well at the moment, he's in prison for statutory rape."
General Drayfox:"What? RAPE?"
Mayor:"Statutory rape! It was an accident, she was wearing makeup!"
Drayfox:"Uh - I really don't think that's any excuse!"
Mal also makes a number of jabs at Inara's job, which he refers to as prostitution. Interestingly, it stops at insulting the job, seeing as he treats his other female crew members with respect, is perfectly fine with the prostitutes he's hired to help in "Heart of Gold", and decks a guy for insulting Inara herself.
Jayne objectifies women pretty much non-stop, is rude towards both Wash and Simon for being wimpy and is... less than kind to the mentally ill.
Married... with Children gave us Al Bundy and played it for laughs. Al was by no means a racist (he even had at least one close friend who was African-American), but he was always quick to ogle beautiful women, mock his obnoxious customers for their weight, pick fights with the feminist-minded Marcy and generally say whatever was on his mind no matter who would be offended. Al even founded NO MA'AM (National Organization of Men Against Amazonian Masterhood). In one episode, he returns from a quest with a series of commandmants - "Rules for hard-working people, who don't give a rat's ass about political correctness!" (To tell the truth, Marcy really wasn't much better than Al. She fell into the All Men Are Perverts trope. In fact, the show seems to have almost no characters with outstaning redeeming features at all, which is kind of the point.)
Radio
Big Wayne from The Lazlow Show is generally the comedic center of the show, but he is horrifically pick-one-ist, and an entire section of the show involves him discussing his terrible exploits with women.
Roleplay
Trigger in Dino Attack RPG, who admittedly drew some inspiration from Jack Crow. Of memorable note was his openly criticizing Hotwire and Rex for continuuing to fight despite losing their leg and being unable to walk, respectively (although he did at least try to justify this by pointing out the impracticality of putting a wheelchair-bound agent in a combat role on a tropical island- usually a very wheelchair-unfriendly environment).
Soldier acted as a more comedic version- he's extremely sexist, but has a tendency to make insulting remarks about women in front of Maria, a very active feminist.
Additionally, Agent Andrew "Pyro" Jackson was eventually revealed to be extremely homophobic, to the point where he disowned his own daughter.
Tabletop Games
Just about everyone in Warhammer 40000 is horribly prejudiced against everyone else, hero or otherwise. Of course, being the Crapsack World that the 41st millennium is, bigotry is basically required not only to survive, but to avoid a horrible Fate Worse Than Death that will last for all eternity.
The Imperium of Man's official state policy espouses Absolute Xenophobia, and the only reason they haven't completely genocided every alien race in the galaxy is because humanity is already struggling enough just to survive. Mutants have it only slightly better, since the Imperium needs psykers in order to continue functioning, but those who haven't been sanctioned as Imperial servants are fair game. Justified since a rogue psyker is vulnerable to daemonic possession and can lead to tens of billions of people getting their souls swallowed.
The Eldar view themselves as the superior species and look down on everybody else. In fact, they will gleefully cause the deaths of billions of another species just to save a handful of their own.
Theatre
Fiddler on the Roof is set before women's lib caught on in the Ukrainian hinterland. Tevye is, undeniably, a big ol' chauvinist, but he's the nicest incarnation of it that you'll find.
Video Games
Renegade!Shepard can be quite racist. Some of the squad members edge into Noble Bigot territory: Ashley believes humans should be able to stand on their own, and is hesitant about placing too much trust in allies from other species, while Garrus can be pretty insensitive in his conversations with Wrex and Tali (he wises up).
In Mass Effect 2, one of the artifacts at the original Normandy crash site is the personal journal of the deceased X.O. Presley. Over the three pages that survive, his attitude shifts from one of blatant xenophobia to grudging acceptance to complete trust in his alien fellow crew members as well as shame over his old attitude displayed on the first page.
Varian Wrynn and Admiral Proudmoore fall afoul of this in Warcraft due to their racist attitude towards orcs. The problem with them being vilified is that in the setting, their entire world was nearly destroyed by orcs, and damn near everyone has been in a near-apocalyptic conflict of some sort. Yet racism is held up as The Big Evil.
Maybe because of the fact that the orcs are not really evil but were manipulated at the time? If they stopped with the racism, they might actually learn to live together and solve far more of the worlds problems than they are able to right now, take a look at the battle of Mount Hyjal, for one.
Proudmore lived and fought through the Second War. His eldest son was killed by an orc-controlled dragon. It's no wonder he hates them so much.
A bunch of orcs enslaved Varian Wrynn while he was amnesiac and made him fight as a gladiator. Then during a peace talk with Thrall a brainwashed Garona — the very same half-Orc assassin that killed Varian's father — tried to kill him. Varian's belief that orcs are Always Chaotic Evil is pretty understandable.
Uther has similar racism against the Orcs, also caused by bad experiences with them. He is one of those who gets Tirion exiled for trying to help save Eitrigg, an orc, from being executed, and tells Arthas that if he pursues vengeance, he will be no better than the orcs.
Duke Nukem is the embodiment of this trope Played for Laughs. He's a hyper-masculine tough guy who hates aliens, loves beer and strippers, and doesn't give a rats ass about political correctness.
Jonatham Ingram in Policenauts comes across as one of these in the fan translation, due to casually using the word 'faggot' and calling biovestites 'so-called "women"'. The heroes are all rather bigoted towards the Frozeners (genetically-altered humans with paper-white skin and unblinking eyes), and it is not really challenged.
Lampshaded in the webcomic The Beevnicks, where paterfamilias Tom Beevnick, a constant horndog, literally won a lawsuit to allow him masturbation breaks at work (presumably to reduce his constant sexual harassment of his female coworkers).
Subverted in Futurama with Zapp Brannigan, who is perceived in-world as a Magnificent Bastard, but to the main characters and the audience is just a Too Dumb to LiveJerk Ass in velour. In one episode, it is revealed that women are no longer allowed to serve in the military, not because of some societal prejudice, but to prevent his constant sexual harassment.
"Alas, after a series of deadly blunders caused by distracting low-cut fatigues and lots of harmless pinching, the army decided women weren't fit for service. Not when I'm in charge."
The Professor has a hint of this. When Fry thought he was a robot:
Leela: "I'm going to remind him he's human the way only a woman can."
Farnsworth: "You're going to do his laundry?"
When stuck at Roswell in 1947, Leela and the Professor dressed in hilariously stereotyped clothes go to an appliance store to acquire a microwave oven, not realizing they aren't invented yet. While the salesman ignoring Leela and focusing his pitch to her "husband" could be somewhat handwaved as the sexism prevalent to that era, the Professor gleefully partaking in the jokes certainly wasn't excusable, as Leela reminds him by setting his tie on fire with an oven.
Pakku from Avatar The Last Airbender held sexist values for most of his life. When he was a teenager, his bigotry caused his fiancée Kanna note Katara's future grandmother to leave him. After realizing this as an old man, he realizing that his ideas were wrong and starts to see women as equals. (For example, he trains Katara in combat waterbending, even though traditionally, female waterbenders are only allowed to use their powers for healing.) He even meets up with Kanna again, and after she realizes that he's changed, Kanna marries him, making him the grandfather-in-law of Sokka and Katara.
Sokka is a bit sexist for the first few episodes, believing that women should Stay in the Kitchen and out of the fighting. Which is somewhat justified as his father, the chieftain, left him behind with the women and children when all the other men went to war. To comfort him, he told him that it wasn't because he was too young but because someone would have to stay and protect the village and he should be honored to be entrusted with this important duty. After getting to know a group of female warriors who have actual training and experience as soldiers and are much more skilled than him, he starts to adjust his views, though it still takes some time to completely get over his prejudices.
Teen Titans the Titans team up with alien super hero named Val-Yor at first he was a nice guy to the Titans, but later he shows prejudice against Starfire, as he has some hatred towards Tamareans, and berates her for almost every move she makes. He also calls her "troq" which means "nothing".
Accidental Genius Bonus: In the Shakespearean years, the word "nothing" was a slang term for, well, a woman's place, so...
In The Princess and the Frog, Naveen looks down on Tiana for being a waitress (he initially thought she was a princess, and believes that she tricked him). He also flirts with a number of women when he's fixing to get married, and a deleted line has him saying "I don't take advantage of women. I give them pleasure." He gets over it as the movie progresses, and Tiana teaches him to be less of a hedonist.
Cotton Hill in King of the Hill is a racist, sexist military veteran with a grudge against Japan due to the loss of his shins while facing them in the Pacific Theater during World War II. He gets somewhat better over the course of the show, which also reveals that he was in love with the Japanese nurse who cared for him after the war.
This was the entire point of The Simpsons episode "Homer's Phobia". Homer was incredibly homophobic, which was shown after he met John, but did mellow a bit after John saved his life. John summed it up rather well at the end:
John: Well, Homer, I won your respect, and all I had to do was save your life. Now, if every gay man could just do the same, you'd be set.
