Played more literally than usual in the Territory Arc in YuYu Hakusho, wherein one of the characters with Territory abilities can create a Territory in which violence is not possible, and the only way to beat the other person is to make them say whatever the Taboo might be at the moment. Kurama talked him into making the whole Japanese alphabet taboo one letter (kana) at a time, then made him laugh—setting off several of the Taboo sounds and beating him at his own game.
Also one earlier in the Four Saint Beasts Arc, where at the end Hiei notes that Kurama has to have the last word.
In Corsair, Aura, princess of a pirate clan, is kidnapped by the governor-general of a nearby territory, Jean-Hughes D'Aubigne. Their first conversation with her as a hostage consists of them sharing a meal and speaking in polite monotone while exchanging sentiments such as "It's hard to believe a beauty like you is also a dirty sea pirate."
In Black Butler II, those meetings between Sebastian and Claude that don't degenerate into an outright brawl inevitably turn into this, as they exchange backhanded compliments and critique each other's buttling-skills.
Used quite in a while in Oniisama e..., specially by Rei and Kaoru when the first is in her rare good moods, by Mariko and Aya when they can't slap each other around, or by Fukiko against whoever she's displeased with.
Megumi has been bullied by Miki all her life, but she knew she cannot defeat Miki in a physical confrontation, so she has adopted a Combat Pragmatist philosophy and never pass on a chance to verbally humiliate Miki… at the price of developing a terrible Guilt Complex: Megumi is so a Bitch in Sheep's Clothing that she believes herself a Card-Carrying Villain due to her self-hatred.
America and Russia in Axis Powers Hetalia are shown to do this. Most notably with their exchange in the America's Birthday strip, where Russia gives America a huge box of "extra small" condoms and a one-way ticket to Siberia. This conversation ends with them laughing while an intimidating aura emits from both of them.
The characters in Archie Comics engage in this from time to time.
Katy Keene has this, especially between Katy and Gloria, often about each other's clothes. One cover has Gloria implying her dog is barking at Katy's white mink wrap because it is really cheap cat fur, and Katy says that's odd since the dog is owned by a cat.
Emma Frost's relationship with most of the other X-Men tends to be this trope.
The second season of Children Of Time has two running examples: the Holmeses vs. Chief Inspector Grayson (Beth Holmes's boss), and the Holmeses vs. Professor Moriarty.
The first Iron Man movie has a wonderful little example between Pepper Potts and Christine Everhart.
Pepper:(after Stark's one night stand with Christine) I have your clothes here; they've been dry cleaned and pressed. And there's a car waiting for you outside that will take you anywhere you'd like to go.
Christine:(patronizing tone) You must be the famous Pepper Potts.
Pepper:(smiles and nods) Indeed I am.
Christine: After all these years, Tony still has you picking up the dry cleaning.
Pepper: I do anything and everything Mr. Stark requires. Including, occasionally, taking out the trash. Will that be all?
Kato takes this attitude with Britt when the direct approach doesn’t work: He goes on a date with Casey and lies to Britt about visiting his friend Tony. Does it not seem suspicious that the Hypercompetent Sidekick risks letting his Man Child employer near a gas gun?
Pretty much everything by Jane Austen is made of this trope because they're about snarking on a society that reveres manners (so most conflict is dealt with in the most cutting — but polite! — manner possible), but Pride and Prejudice is probably the best example because of all the people who disapprove of the couples and make it known in the most polite way possible.
Someone once re-wrote Dirty Harry in the style of Pride and Prejudice. "Dirty" Harriet Bennett ends up telling Lady Catherine de Burgh "I have no objection, Madam, to your proceeding, since by doing so you shall render my day perfectly agreeable."
A refrigerator is also the site of Passive Aggressive Kombat in The Long Dark Tea-Time of the Soul... Dirk Gently does not want to open it before his housekeeper cleans it, and sets up elaborate, tiny traps in order to be able to tell if she has, one including a strand of hair. The refrigerator turns out to be so epic in its filth that it spawns a horrible god-eating abomination when it's finally opened.
Cersei Lannister is much more accomplished at this, as when she tells Margaery Tyrell that she's "never seen her as a rival," which Margaery (publically, at least) takes as a denial of ill-feeling between them but which Cersei intends as implying that she does not view Margaery as a worthy opponent.
Downton Abbey, being set in a British manor house in the early 1900s, is chock full of this. Mary and Edith, and Violet and Isobel, are the particular champions. When Cora's mother shows up, however, she and Violet play for the World Cup Final, US v UK.
Sherlock's brother Mycroft and best friend John in Sherlock are never downright rude to one another, and seem generally resigned to working together for Sherlock's sake. While they are allies, they're clearly not on friendly terms, and things can - and do - get snarky and hostile at times. John tips closer to the 'aggressive' end of passive-aggressive in The Reichenbach Fall due to the knowledge that Mycroft, in an attempt to get Moriarty's master keycode, ended up giving the Diabolical Mastermind exactly what he wanted: Sherlock's entire life story.
In Arrested Development, Lucille and Lucille II engage in this as "primary social rivals", usually these encounters get less subtle and less passive as they go.
Farscape: War Minister Ahkna and Commandant Grayza meet in private to discuss a potential treaty, without the knowledge of their superiors. While they are clearly enemies, they manage to maintain a polite(ish) facade, with only occasional barbs about Ahkna's inability to get promoted of late and Grayza's use of her body to get ahead.
Game of Thrones. Loads of this in Season 3, as Tyrion and Cersei Lannister find themselves sharing power in King's Landing with politically-astute House Tyrell, plus their all-powerful patriarch of a father, Lord Tywin Lannister. Snarky comments are sometimes the only defense they have left.
The duet "Via resti servita, madame brilliante" from Wolfgang Amadeus Mozart's The Marriage of Figaro involves an exchange of politely delivered insults between Susanna and Marcellina. The latter storms out after Susanna wins by "congratulating" her on her old age.
Happens a lot in the TouhouUniverse CompendiumSymposium of Post-mysticism. The symposium section is composed almost entirely of three characters taking snipes at each other while explaining how their world works.
Nessiah from Yggdra Union and Blaze Union is as sharp-tongued as he is short-tempered (which is very), and isn't one to let an insult slide. This is a lot more apparent in Blaze Union as Nessiah has more screen time there, but he's still passive-aggressive as anything in Yggdra Union too. For instance, take this discussion with that game's protagonists (who have just committed mass genocide and killed a number of people Nessiah cared about) concerning a character Nessiah brought back from the dead:
Nessiah: It was an awfully thankless task, gathering up every last scattered piece [of her body]. *giggle* But it's quite all right. Wherever anything was missing, I was able to substitute other parts. You left quite a lot of those parts for me to work with...
In Katawa Shoujo, Lilly and Shizune get into a rather heated war of words over the punctuality of the submission of reports for Student Council activities before the school festival. However, as Shizune is deaf-mute (and Lilly is blind), Misha is at hand to translate everything she conveys, and doesn't quite grasp the true context of what the two are actually saying, which diminishes the effect somewhat.
Lilly: I was actually just discussing the budget report before you came by. You must be very talented to have finished all your student council duties so quickly that you can track me down to make sure I don't forget my own. Misha: [translating for Shizune] Are you accusing me of slacking off? It seems like you're confusing me with yourself~! Lilly: I don't think so. That would be a very difficult thing for me to do: comparing myself to you. Misha: You're right, the difference between us is like heaven and hell. Lilly: And it's not hard to guess which one you might represent.
Poor Hisao, who's much more contextually aware, is also tapped once to translate a conversation between the two. His attempts to modulate the argument prove futile.
The exchange between Franziska and Mia (channeled by Pearl) at the start of the second trial day in case 2-2 is a nice example (slightly undermined by von Karma's foolish foolery, though Mia remains civil), even lampshaded by Phoenix:
Franziska: The image of your defeated face will be transmitted all over the world! Mia: All over the world, huh? Sounds like you've made quite a name for yourself, Phoenix. Franziska: Don't be foolish, you foolish fool wearing the foolishly foolish clothes. The famous one is me! I'm the prodigy who has never lost a case since becoming a prosecutor five years ago. Naturally, the world's eyes are on me, as I conduct my first trial in this country! Mia: Uh, huh... That's nice, Ms. von Karma. Franziska: Hmph. Glad to see you're in such good "spirits" today, Ms. Fey. Phoenix: (Uhh... It's true what they say... Women really are scary when they fight... *gulp*)
Interestingly enough, Mia is far more forthcoming about how little she thinks of Edgeworth during their first trial, and Franziska tends to repeatedly call people fools when she's not using her whip.
Morgan Fey's interactions with most people involve her doing this, as she tends to address others with superficial politeness and humility, but is actually quite condescending.
Lotta: Hold on, now, granny!
Lotta: How come we ain't allowed in that room!?
Morgan: Dear madam, you have an "impressive" grasp of English. From where did you learn it?
In one arc of Bruno the Bandit, Bruno encounters a gang of pirates who wield weaponized passive-aggressiveness. They do it with the help of magic rings that make other people unreasonably concerned about what the pirates think of them.
Something Positive: If they could make money at it, this would be the family business of the McIntyres. The champion in the family is, generally, agreed to be Faye.
Characters in Rumors of War use conversation as their primary mode of aggression.
Subverted at the end when the father calls his wife a whore in front of their child.
Tom Tucker and Diane Simmons jab at each other with passive aggressive comments on live television and the comments grow more and more demeaning in each episode as their disdain for each other gets more intense.
My Little Pony: Friendship Is Magic, "Look Before You Sleep": Rarity and Applejack end up stuck at Twilight Sparkle's place during a thunderstorm, and end up doing a bit of this thanks to residual bad feeling from an earlier argument.
Rarity: Fortunately, I can get along with anypony, no matter how rude she may be.