The Sitcom Arch Nemesis is a very different creature from the dramatic or action-show Arch-Enemy. He usually isn't dangerous or evil; for the most part he's just very annoying and sometimes he's a Nice Guy. He just rubs a character from the show (usually the lead) entirely the wrong way, and the two will never miss an opportunity to have at each other. Often the character and his nemesis are both kindred spirits and don't realize it; these rivals are much more likely to have an Enemy Mine plot than dramatic rivals.
This character is rarely part of the main cast because if they were then The Protagonist would do nothing but fight with them. Exceptions are on the analysis page.
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Anime and Manga
In the various versions of the anime/manga El-Hazard, Jinnai always has this near-psychotic hatred of Makoto, school ace and a Nice Guy to boot, who easily makes friends with anyone, including Jinnai's own sister Nanami. It also doesn't help that Makoto is too nice to notice that he's been beating him in almost every aspect without even trying.
Subverted in A Little Snow Fairy Sugar: Greta considers Saga to be her rival in all things, but Saga, who is uninterested in rivalry, pretends to be completely oblivious to Greta's challenges and boasts.
France and England, so much that there's a "French-English Quarrel Preserve" and England gets involved in The War of the Austrian Succession just to fight France. It's said that antagonizing each other is the only thing that keeps the two old timers going, and of course, it's Truth in Television.
Greece and Turkey too, and in fact Turkey is the only thing that makes the usually laid-back Greece get riled up at all. Also, Hungary and Romania.
Russia and America are this after the Cold War. Though they're no longer enemies, they're still very passive-aggressive towards each other.
Cowboy Andy from Cowboy Bebop, who is a rival bounty hunter in it for the glory. Spike hates him, and spends more time fighting off Andy than he does actually trying to catch the episode's bounty. Faye and Jet realize that this is because the two men are too similar: Both are impulsive, petty, tend to jump to conclusions and have a penchant for causing wanton collateral damage.
Gash Bell's enemies numbered among them a demon who could brainwash other humans, a giant mindless destruction machine... and a weird-mouthed human girl who delighted in tormenting him. Somehow, that last one was a challenge he never overcame.
The title character has Yanda, whom she instantly hates with a hatey five-year-old hate, but other characters merely find annoying. It doesn't help that Yanda takes a childish glee in figuratively (and literally) yanking her pigtails.
Jumbo almost has this sort of relationship with Miura, of all people. At one point, he flies to Hawaii just to spite her.
Piyoko from Di Gi Charat and the Digi Devil from Panyo Panyo Di Gi Charat really try to be legitimate Big Bads, but being inept villains in humor series whose schemes rarely rise above the level of Poke the Poodle dooms them to be this instead.
Watanuki from Xxx HO Li C hates Doumeki for no adequately explained reason, simply stating that he's thought of Doumeki as annoying from the moment he laid eyes on him. Unfortunately for Watanuki, Doumeki is also a living spirit repellent, while the whole plot of the manga was set in motion because of the fact Watanuki's very blood attracts spirits, so he's often forced into Teeth-Clenched Teamwork with Doumeki. Further complicating matters, several people in universe seem to ship him with Doumeki, including his boss and the girl he likes, and it's implied that Doumeki is not adverse to the idea.
In Kekkaishi, Shigemori and Tokiko spend their mornings attacking each other with gardens hoses; it's part of their feud about the 'legitimate heir' of the Kekkaishi founder. Both are rather upset that their grandchildren don't share their grudge.
A rare mutual form can be found in Yozora Mikazuki, a brunette Jerkass extraordinaire, and Sena Kashiwazaki, a ridiculously hotRich Bitch. Yozora loves heaping verbal, emotional or sometimes physical (by way of a flyswatter) abuse upon Sena until the latter storms off crying; Sena in return loves showing off how rich, beautiful and hot (not to mention huge-breasted) she is compared to Yozora. But at the end of the day, both are Not So Different, being friendless girls who tend to agree on anything they, ironically, are Comically Missing the Point on.
To a lesser extent, Kobato Hasegawa, a 13-year-old Elegant Gothic Lolita, and Maria Takayama, a 10-year-old nun, who engage in outright childish fights over the attention of the former's older brother, Kodaka.
In My Bride Is a Mermaid: Lunar tends to treat Sun this way, though Sun doesn't really reciprocate and simply views Lunar as a friend. Mikawa and Nagasumi's relationship basically oscillates between this trope and The Rival before eventually settling into Vitriolic Best Buds territory.
The "Super Buddies" (a group of losers Formerly Known as the Justice League) had a pair of neighbours building a bar next to their headquarters. One of them was Richard "Dick" Hertz; Sue hated him when she found out that he was once the supervillain Blackguard (who?), who worked for the "1000" in Metropolis (oh, that Blackguard, sure). Oh, and Dick had an associate in the bar, who was once the greatest American hero, or so he says — Guy Gardner
Humorously, Blackguard was a recurring enemy of Booster's in his early solo career, but neither seems to remember the other.
Donald Duck and his neighbor Jones (essentially a larger human version of Donald with no relatives other than a rarely-seen mother).
In Hack/Slash, extradimensional talking mutant dog Pooch claims he is constantly tormented by an innocent-looking pug named Goblin. We never see this in action, but from the way Pooch talks about him it's clear that their relationship is one of intense animosity.
In The Life Aquatic with Steve Zissou, Steve perceives that he has a professional rivalry with Hennessy, but it's pretty obvious that in reality the former is simply bitter that the latter is a more successful oceanographer, the former husband of Steve's ex-wife and kind of a jerk.
In Office Space, Michael Bolton feels this way about Michael Bolton.
In the Discworld book Snuff, Lord Vetinari appears to have reached this level of 'enmity' with the crossword editor of The Times, whose mastery of obscure linguistics and terrible wordplay is advanced enough to give even him pause.
As of Raising Steam she has landed several victories, but the stress of the contest finally gets to her and she resigns.
In the first chapter of Lunar Park, Bret (in a semi-fictionalized account of the author's real life) takes several personal shots at Keanu Reeves.
Jerry also had Kenny Bania although that was one sided as Jerry was Bania's idol.
Likewise, George had Lloyd Braun, while Elaine had Sue Ellen, "The Bra-less Wonder".
Kramer had FDR... Franklin Delano Romanowski.
Unusually for a sitcom, a recurring character had an arch enemy. Jack Klompus was this to Jerry's father Morty.
As the description says, Mimi and Marcy are main characters who are these. In fact, because they are main characters, they are more frequent sources of the Enemy Mine.
In Frasier, Frasier had Cam Winston. The two were virtually identical to each other, in that they were pompous, snooty, articulate egomaniacs. When they finally called a truce because they thought their parents were dating, their "treaty" included them agreeing to share grooming and personal care advice on features the other one had noticed.
Bill: Hasn't this been done before? I mean, every year some billionaire goes up in a balloon.
Mr. James: Why do you think I'm doing this? The peer pressure among billionaires is tremendous. Bill Gates practically called me a Nancy-boy.
In Dad's Army, Captain Mainwaring (the pompous, upper-middle-class bank manager whose power and authority as Home Guard platoon leader has gone straight to his head) has Chief ARP Warden Hodges (the pompous, lower class greengrocer whose power and authority as Chief ARP Warden has gone straight to his head).
In Cheers, Sam's nemesis was the rival bar "Gary's Old Town Tavern".
Also John Hill, owner of "Melville's" the restaurant upstairs.
Carla also considered Diane to be her worst enemy with Cliff perhaps a close second.
Woody had his father-in-law Mr. Gaines.
Mr. Bean had his sadistic grudge against that blue Reliant Regal car.
His diary features a similar relationship with the Man in Room #3 down the hall, told entirely through the notes that he leaves outside the door and Bean sticks in the book. They decide to bury the hatchet (literally!) on New Years Eve.
Blackadder had an interesting one; Edmund Blackadder himself was the Sitcom Arch Nemesis for most of the series. Captain Darling in Blackadder Goes Forth is this trope played straight and the same could apply for Melchett in Blackadder II.
In Scrubs, J.D. has the Janitor and, briefly, hotshot intern Keith.
J.D. and Sean also don't much like each other. What with stealing each others girlfriends.
In Father Ted, the titular character has Father Dick Byrne. The two constantly get into ridiculous one-upmanship contests, not realizing how similar they are; one episode ended with a split screen of their two households, with identical action going on on both sides.
Mrs. McClusky on Desperate Housewives started out as this for Lynette, but ended up as a subversion as the two eventually came to understand each other as the series went on and formed something of a friendship.
There's also Susan vs. Edie.
In That '70s Show, Red Foreman's arch-nemesis is Bob and Midge Pinciotti. Something of a subversion, as, for as much as Bob annoys Red and Midge annoys Kitty, the two are probably the couple's closest friends.
Also, Mitch and his father are enemies of Eric and Red. This was a subversion of the "actually very nice" example, because, as they started losing battles, they revealed their problematic relationship. In later appearances, Mitch was reduced to a joke.
The UK version of The Office had Tim vs. Gareth. The US version has Michael against Toby and Dwight against Jim; in the former case, Toby looked upon Michael's "rivalry" with a measure of disbelief, and in the latter case, Jim uses it as an excuse to constantly pull pranks on Dwight. A somewhat more straightforward rivalry in the US version was Dwight vs. Andy, first when Andy attempted to usurp Dwight's position as Michael's favorite and later when both got involved in a love triangle with Angela. They have since become fairly good friends. In later seasons, the Andy vs. Nellie rivalry replaced the Andy vs. Dwight one.
In Grounded For Life, Finnegan had O'Keefe as a nemesis. Their children were dating. Also, Finnegan's bar had "McGinty's".
Also in season one, he has a one-sided rivalry with Robin's two main love interests - Sandy Rivers and Derek.
Also Robin has Patrice her co worker at World Wide News
NOBODY ASKED YOU, PATRICE!
On The Dick Van Dyke Show Buddy Sorell made every attempt to insult producer/ bald brother-in-law of the star Mel Coolley.
It's also Lampshaded that their enmity is totally idiotic. Buddy's explanation for why he keeps making fun of Mel is "I do it 'cause I like to rib him! And..I sort of...hate him."
Stan Sitwell to the Bluth Family in general, and George Sr. in specific. Subverted by the fact that he is a genuinely nice man who is largely oblivious to the extent of the Bluths' disdain for him, and that George dislikes him because he is in the same business and just as successful (without the need to resort to illegal practices), and his philanthropy makes the Bluths look bad. George and Lucille even went so far as to adopt a daughter they didn't want (Lindsey) who Sitwell was trying to adopt, purely to spite him.
Lucille also had Lucille 2, her very nice neighbor who wanted nothing more than for the Bluths to succeed. Once, Lucille 2 hired some construction workers to renovate her apartment while she was away, and Lucille wound up getting them to move the wall dividing their homes two feet in, and install a larger bathtub for her.
In Chuck, Season 1 had Harry Tang, arch-nemesis to Chuck and Morgan at the Buy-More. Season 2 had Emmit Milbarge fill the role (and how spectacularly he did).
On Full House, once Michelle takes over the Little Miss Snarker title from Stephanie, Stephanie redirects her snide remarks towards Kimmy, who only occasionally fires insults back due to her relative lack of wit. In fact, of all of the main cast who ever makes fun of Kimmy, Stephanie does it the most often — sometimes multiple times in a single episode.
In Reba, Brock has not one, but two nemeses — Eugene (a rival dentist) and Lori Ann (Reba's friend). Both of them are eventually Put on a Bus.
In Monk, Adrian Monk has Harold Krenshaw, who shares a therapist and many phobias and neuroses with him. The rivalry is mutual, usually over who is better friends with the therapist or who has made more progress.
The Big Bang Theory's Sheldon Cooper actually has two of these, the first being Barry Kripke, who he once got in an Escalating War with (it didn't end well), and the second being Wil Wheaton. The latter has had a showdown with Sheldon twice and Wheaton triumphed both times. However, he used underhanded tactics both times. You might count the Indiana Jones showing as a third occasion, meaning Sheldon has one victory.
Shelly is just great at getting arch nemeses. There is also Leslie Winkle: who "made Sheldon Cooper cry like a little girl?".
Sheldon's childhood idol Arthur "Professor Proton" Jeffries has Bill Nye the Science Guy (who actually admires him) for ripping off his show.
In Home Improvement Tim's hated rival Bob Vila made several guest appearances, often dismissing Tim's show as a ripoff of his own.
Tim shows a surprising bit of maturity after a race when he reveals to his wife that he could have won but let Bob win as to do so would have been at extreme risk of destroying the car. Bob bought his car and would just get a new one, Tim built his over the course of a year and wasn't going to throw all that work away just to prove a point.
Tim also hated the nearby but never seen Doctor Johnson, an 80 year old proctologist who won the Christmas lighting competition every year. Considering the lengths Tim goes to beat him, the doctors display must have been quite a sight indeed.
Alternatively, Tim's exceptionally overdone and usually dangerous displays may actually have been illegal in the contest (leading to disqualification) and the good doctor was the best of the legal entrants. Given that one year, his display was bright enough to enable a plane landing, illegal is likely. (Then again, they won that year.)
From Half And Half Big Deedee Thorn regularly competes with her husband's ex-wife Phyllis. She also has an evil sister.
In Parks and Recreation, there is an extremely bitter rivalry between the parks department and the library department, as well as the entire city of Pawnee with Eagleton (though it's mostly one-sided).
iCarly has two pairs: Sam with Freddie, and Carly with Nevel.
In Coupling, Patrick has Ivan, who is like the uber-Patrick, complete with snazzy car, corner office and blonde trophy wife.
Modern Family plays with this trope in the episode where Cam is hosting a charity function for a music appreciation group. He keep referring to his rival (who hosted the event the year before) as his new nemesis. Mitchell tries to point out that it's just silly in real-life, but Cam takes great delight in the drama the relationship allows for.
Played straight with Jay and Manny's father, Javier.
Community has Jeff's rivalry with Rich, the handsome doctor who is always better than him.
The gang also hated Shirley's unseen friend Gary and absolutely loath Todd Jacobs, Greendale's resident Nice Guy.
Everybody Loves Raymond Ray actually calls Peggy, the leader of his daughter's scout troop and mother of her best friend, his "arch enemy".
The rivalry between Debra and Marie can be seen in this way.
Marie thinks that Harriette Lichman is her archenemy for Frank's affection. Frank casually toys with her on that.
Raymond occasionally banters with his neighbor Parker despite Ally and Parker Jr. getting along nicely.
Robert and Raymond's sibling rivalry borders on this a time or two.
Peter, Robert's brother in law started out as this. Ironically his sibling rivalry between himself and Amy has been known to mirror Raymond and Robert's. Not to mention he is currently dating Raymond's arch enemy Peggy.
Debra and her sister Jennifer are revealed to mirror Ray and Robert. In this case Jennifer was the favoured sibling, possibly explaining Debra's affinity with Robert.
Town selectman Taylor Doose from Gilmore Girls generally only exists to annoy the main characters, and generally the whole town of Stars Hollow with his obsessive need to control every aspect of the town. Luke in particular sees him as an arch nemesis.
On Just Shoot Me!, Jack is constantly competing with Donald Trump over who is King of New York. Also regular is head photographer Elliot with Annie Leibowitz. Occasionally, the entire cast and Cosmo magazine.
On the short-lived sitcom Hope And Gloria, talk show host Dennis Dupree (Alan Thicke) has a massive grudge against, um, actor Alan Thicke. This comes to a climax at a Growing Pains reunion on Dupree's show which ends in a Thicke on Thicke fistfight.
On NUMB3RS, we meet Marshall Pennfield, Charlie's old rival from Princeton. Near the start of the episode, he performs a lecture in which he finds a flaw in the Eppes Convergence, the mathematical theorem that made Charlie famous. Charlie will readily admit that Pennfield is brilliant; he just doesn't like him because he's an asshole. In the end, Pennfield helps Charlie figure out the case of the week, and while Charlie does find a way around Pennfield's problem, he calls it the Pennfield variation.
Averted with Roy Slater on Only Fools and Horses. He's presented in the context of this trope, but is genuinely villainous. He's a Dirty Cop, a borderline-abusive husband, and a sociopath.
In Noob, Omega Zell is The Team Wannabe to Justice guild, but also a self-centered He-Man Woman Hater. Saphir, the person who gets to call the shots on whether or not he gets in, is basically an Iron Lady with a little of The Perfectionist mixed in. Their personal interactions shown in the webseries and mentionned to happen in the novels are conflictual, but their respective guilds remain allies to each other.
Another nemesis was Rosalyn the baby-sitter, who was the only person Calvin actually seemed to fear.
With Moe, things balanced out in a cosmic sort of way. Calvin ran intellectual circles around Moe, but Moe had the raw physical power to make that not really matter that much in the immediate short term.
Bucky from Get Fuzzy has Fungo, the ferret that lives next door. It's probably safer to say Bucky is Fungo's Sitcom Arch Nemesis, rather than the other way around. Bucky seems to dislike Fungo (and ferrets in general) on the basis that they're too clever by half, and attempts to wage a campaign of harassment against Fungo; Fungo, on the other hand, doesn't really seem to care much about Bucky at all, outside of subverting Bucky's gambits by being too clever by half.
Peanuts has Snoopy and the vicious "Cat Next Door". The cat is never seen, but routinely rends Snoopy's house with a single swipe of it's claw as a response to his cutting witticisms.
Charlie Brown and Lucy could be considered this.
Lee Ann Womack's song, I'll Think of a Reason Later describes this toward a woman that the singer hasn't even met, but is apparently engaged to a man she likes. She concludes, "She may be an angel who spends all winter/Bringing the homeless blankets and dinner," but "I really hate her/I'll think of a reason later."
The Lonely Island have this as a running joke in their "Just 2 Guyz" series of music videos (which also includes "We Like Sportz", "We'll Kill U", and "We Need Love"). The two protagonists, Guy Number One and Guy Number Two, despise their neighbour Steve (played by Andy Samberg), calling him a cunt in each video (except "We Need Love", where they instead accuse his girlfriend of being a slut)—despite him never being seen to do anything malicious to them.
The first season of GLOW featured plenty of examples of the "dramatic", but it also featured Americana and Spanish Red, who had much in common, in spite of open hostility and did indeed have enemy mine situations.
On a promotional level, ECW and the World Wrestling Federation. On screen, they were antagonistic to one another. Off screen, they actually worked together against main rival WCW. This was also true of ECW and Smokey Mountain Wrestling but it lacked a national TV deal so no one remembers it.
CM Punk and Delirious had many legitimately bitter feuds in IWA Mid-South. Their feud with each other was not one of them. The wrestling was serious enough for one hour time limit draws but their personal attitude towards each other was mainly down to who had the best pranks.
Phil Harris, of the radio sitcom The Phil Harris Alice Faye Show, had two of these on his show: his brother in law Willy and the grocery boy Julius, who is in love with his wife, Alice.
In the first season of Mitch Benn's Crimes Against Music Mitch's arch-nemesis was Richard Stilgoe, especially as Robin Ince mentioned Stilgoe whenever Mitch referred to himself as The BBC's most popular satirical songwriter. They eventually battled it out in the final episode of the season, and became friends.
Mitch: Looks like I'll need a new arch-nemesis for the next series. Richard: Is Bill Bailey ready for this?
A very dark version from Cabaret in the form of the promiscuous Fraulein Kost, who turns the play's extremely sympathetic Jewish character over to the Nazis, then rallies a bunch of background characters to Nazism in the truly spectacularVillain Song that closes act one. Her motive in doing this? To spite her landlady.
Raul Tejada and "Best Friend" Tabitha in Fallout: New Vegas. In the Black Mountain Radio channel, Tabitha is often threatening Raul with execution. However, Raul merely needs to remind her that he has not outlived his usefulness and is the only one who could possibly repair her beloved robot Rhonda (as well as being a useful repairman in general), to her frustration. If the Courier does not complete their quest, the two are still at it for a long time.
Klavier Gavin to Apollo Justice and detective Ema Skye, which is particularly strange as despite being a Prosecuting Attorney (an antagonistic role from the protagonist's point of view), he's very much a good guy, which makes him fall squarely into this trope.
Bob Arnold in Phantasmagoria 2 acts like this to protagonist Curtis Craig (rival employee, seeminglynote Bob's actor has suggested that Bob's jerkassery towards Curtis is partly because he's attracted to Curtis and tries to cover it up really dislikes each other, does pranks, is fighting over a promotion...). Only problem is, Phantasmagoria is a horror story... so Bob gets killed. Horribly, and in a way that puts suspicion on Curtis.
PvP has Max Powers. Cole and Brent hate Powers with a passion, with Francis often joining in on the hate on. It gets to the point his name is the comics' The Khan whenever something goes wrong for Cole.
Later on Cole admits that he doesn't even really have a good reason for hating Max, he's just petty and begrudges Max the fact that he's an overall good guy and more successful than Colenote the only hint of anything less than exemplary character on Max's part, in fact, was an inability to see Skull the troll, and this is hinted to be more self-absorption than any legitimate sin on Max's part. This admission prompts Max to go on walkabout, as the Australians call it, and he eventually comes back with the grating edges sanded off his personality, and the staff of the magazine grow to think of him as a good friendnote and he can see Skull now, too.
In Sluggy Freelance Gwynn seems to feel she and Torg have this relationship at times. Torg actually thinks of her as a really good friend, if maybe a little too hot-headed.
The Inexplicable Adventures of Bob! has Jean and Voluptua. Jean has always considered Volly to be a rival for Bob's affections and resented her for it. After years of ambiguity, her suspicions have now proven to be true.
Problem Sleuth and his next-door neighbour Ace Dick detest each other for unknown reasons, although at the start of the story he does accidentally blockade PS in his office with a bust of Ben Stiller. They continue writing insulting notes to each other and pissing on them until PS accidentally orders AD a load of whores, and AD decides it's time to bury the hatchet and start working together with PS to get out of the building.
Rachel from Dragon City and her neighbor Emily don't like each other, though they got a little better when their daughters became friends and a little better after Rachel became Emily's deputy mayor.
Rachel's daughter, Erin has a girl named Cynthia that she's always feuding with at school.
The Angry Video Game Nerd and The Nostalgia Critic play this to each other. The guys who play them actually get along in real life, but even the character's attempts to do a review together ends in them beating each other up... again.
This is more or less the best way to describe the relationship between Encyclopedia Dramatica and Uncyclopedia, and The Other Wiki too for that matter. (We're the wacky special guest if anything.) Although the former two tend not to bother feuding anymore since given that they're both parody wikis (albeit with entirely different themes) and all involved just look silly.
Inverted in Red vs. Blue, as despite the two sides literally being at war, they act in more of a friendly rivalry, and the only one to actually take the war seriously is Sarge.
On Twitter, Kevin Smith and Neil Gaiman treat each other this way. (In real life, they are friends and fans of each other's work.)
Ryan North of Dinosaur Comics is occasionally this to Randall Monroe of xkcd, explaining xkcd's scorning of North's field of expertise ("Because FUCK computational linguistics"). Like the previous examples, they're really friends.
Meanwhile, North and Andrew Hussie played this to each other for a while, to the point of... well, this. Again, actually friends.
Homer has Ned Flanders, who was almost always jovial and kind in return.
Reverend Lovejoy also feels the same way about Flanders.
Homer also had Frank Grimes, though that was entirely one-sided.
Another one-time example for Homer was being George H.W. Bush in "Two Bad Neighbours".
There is a noted mutual dislike between Homer and Patty and Selma.
Bart has an actual Arch-Enemy in Sideshow Bob (who tried to kill Bart and some family members a few times, so not just a Sitcom Arch Nemesis), but apparently is also an enemy of radio personality Dr Demento.
Principal Skinner is more conventionally a sitcom arch nemesis to Bart.
Mind you, in one episode the two of them fought each other with milk-powered Giant Mecha. Dinkleberg didn't seem to have a problem with the idea.
This is eventually played with in the seventh-season episode "Operation Dinkleberg", where Dinkleberg reveals himself to be completely evil after all and the leader of M.E.A.N. (Ministry of Evil and Abusive Neighbors), only to later reveal to Timmy that it was all an act (that cost him $30,000!) because he knew how much it meant to Mr. Turner to have an arch-nemesis.
Kappa Mikey provides us an odd example, where the lead is the Sitcom Arch Nemesis to another main character. Mikey is utterly oblivious to Lily's seething hatred and jealousy towards him. This is what happens when you put the Cloudcuckoolander and the Alpha Bitch on the same set.
Given the way supervillainy is treated in The Venture Bros., The Monarch and Doctor Venture fall under this trope. The Monarch's aggression is hardly noticed by Venture himself, seems almost completely arbitrary (aside from the fact that Venture made fun of The Monarch's poetry in college), and Doctor Girlfriend has even acknowledged within the show that the two share enough similarities to be good friends were it not for the supposed hatred that exists between them. However, the Monarch has genuine, murderous hatred toward Rusty for reasons yet to be revealed.
The ongoing and largely unexplained hatred of Zoidberg on Hermes' part. It was shown on subtle occasions that Zoidberg was something of an annoying leech to him, as well as his incompetent qualities that Hermes barely tolerates the rest of the team for. Add to that his sheer lack of backbone and he's the ideal stress ball for a traditional bullying employer.
In one episode, Zoidberg claims Hermes is his best friend, as he is the only one who cares enough to insult him even when he doesn't have any reason to, as opposed to the others, who only insult him when he does something wrong.
Zoidberg did once send Hermes to a forced-labor camp. Though the rivlary may predate that, it can't have helped.
Zoidberg did have one with the medical robot in "War is the H-word".
Dexter's Laboratory had Mandark, who is practically the same person as Dexter except more evil. They would have gotten along great if not for both of their egos demanding the other one be their assistant.
This was elevated in a retcon in a later episode, where it is revealed Mandark's entire ascension into scientific study was motivated by getting back at Dexter for laughing at him when they first met. Disproportionate, much?
Stewie/Bertram, Chris/Monkey, and Peter/Ernie the Giant Chicken.
The show seems to be slowly developing Quagmire and Brian into this manner, though it was more of a one sided hatred on Quagmire's part at its earliest points.
Lois' father, Carter Pewterschmidt is rivals with Ted Turner.
And Peter is in bad relations with James Woods.
King of the Hill Hank Hill had... Thatherton! A rival propane salesman who used less than morally scrupulous methods!
He also had a pretty major rivalry with Kahn Souphanousinphone...sometimes.
Scrooge McDuck has many enemies, but his true nemesis is Flintheart Glomgold. They have a similar background, have similar goals, but very different views on ethics and morality. The two are the richest and second-richest duck in the world at any given time. (with Scrooge almost always holding the number 1 spot) Probably the only thing that keeps him from just being a standard Arch-Enemy is that the two do interact with each other from time to time in non-violent settings, resembling a more mundane rivalry.
Bob's Burgers is across the street from Jimmy Pesto's Pizzeria, and the two managers have a mutual obsessive hatred as a result.
South Park has their iconic rivalry with Kyle and Cartman. Cartman is an insane anti-Semitic Comedic Sociopath, Kyle is an over-persistent voice of logic (and a Jew). Their feud ranges anywhere between exchanging childish insults or actually trying to kill each other on numerous occasions.
Francine has a pathological hatred of George Clooney; she spent an entire year trying to get him to love her just so she could break his heart. When that didn't work, she chopped her own hand off so she could escape from some handcuffs to kill him.
Phineas and Ferb: Although Doofenshmirtz is an actual villain and he has a real Archnemesis/Best friend in Perry the platypus, he also has a Sitcom Arch Nemesis in Rodney, a fellow villain. He also has another nemesis in his brother Roger.
Notably, Lawrence also has an "Antiquing Nemesis" in Wellington.
In an upcoming crossover special, Isabella is this to Han Solo of all people.
ISIS as a whole had this sort of relationship with the more competent ODIN, as well as the KGB. They could never quite be real arch-nemesii, as Mallory was in a romantic relationship with the heads of both organizations. However, things seem to have gotten Darker and Edgier between the rival organizations, as Len Trexler (the head of ODIN), was last seen brainwashed and possibly lobotomized by ISIS agents, Major Jakov (of the KGB) has been murdered, and his murderer (ODIN agent Barry) is now running the KGB and is a completely psychopathic cyborg.
Doug Funnie and Roger. Also humorously echoed in Doug's dog Porkchop and Roger's cat Stinky.
Randy Cunningham: 9th Grade Ninja: Brent, the school's metal shop teacher's apprentice, is this towards Howard. He only calls him by his last name and he got upset when he thought Howard was replacing him as apprentice.
Rancid Rabbit from CatDog has a sadist grudge with Cat.
On Regular Show, Rigby feels this way about his brother Don purely because Don has had more success than him and is taller (despite actually being younger than Rigby). This is one sided - Don loves Rigby and wants to spend time with him, and shows absolutely no signs of sibling rivalry with him.
The rivalry between Texas A&M University and the University of Texas has this vibe. A&M students seem to identify themselves more as "not Longhorns" than as "Aggies." Maybe a third of the t-shirts, bumper stickers, and other memorabilia sported by Aggies actually don't say "A&M" but bear anti-UT (which they call "t.u."—no caps—because it's just another "Texas university") slogans and logos (many with biblical references). The A&M fight song, for goodness sakes, is more about insulting UT than building up A&M. Yet UT students don't really think about A&M except when they have sporting matches scheduled—which is not often anymore, given that they are in two different conferences now.
The UT Longhorn logo appears on so much A&M memorabilia—albeit with disfigurements—-that UT had to sue several clothing vendors that cater to Aggies for trademark infringement.
When the tech college note American readers, think "community college", only not so glamorous and well-resourced in Wrexham, Wales, rebranded itself as a university, this led to a lawsuit with a university of the same name in New England. Apparently Yale College, USA, felt threatened by a very minor British new university wanting to call itself Yale University, and alleged this would lead to confusion. Wrexham countered by saying it had been called Yale College for over a century, and had in fact been founded by the same Mr Yale who had emigrated to the USA and latterly had another educational establishment named after him. Alas, Wrexham had neglected to copyright the name. Unlike New England. The court found in favour of the American version of Yale, but it was agreed the Welsh-language Coleg Ial offered no scope for confusion. NEWI Wrexham rebranded itself as University of Wales, Wrexham, or Prifysgol Owain Glyndwr/ Coleg Ial