In one commercial, one teenage boy forces his younger brother upstairs so he can spend time with his girlfriend. The younger brother then uses the TV to show the girlfriend a slideshow of pictures that indicate he's cheating on her.
In the backstory of Saiunkoku Monogatari, Kou Reishin and his friend Houju were both interested in the same woman. Reishin sabotaged Houju's relationship with her by forging a letter from her to Houju saying she couldn't bear to be with a man so much more beautiful than herself. As a result, Houju started wearing masks all the time and calling himself "Kijin," meaning "weirdo," and Reishin married the girl.
Skuld in Ah! My Goddess, who takes her Big Sister Worship towards Belldandy a bit too far and won't stand for anyone, particularly lowly mortal Keiichi, getting too close to her. She frequently sets up booby traps (mostly involving Stuff Blowing Up) to prevent their relationship from progressing. It is hinted a few times, though, that she's acting out not because she's jealous of Keiichi for taking Belldandy's attention, but that she's jealous of Belldandy for getting Keiichi's love.
Makie from Futari Ecchi does that at every opportunity to the main character couple. I.e., she leaves false lipstick marks on Makoto's shirt or calls him in the middle of a date with his wife Yura.
Happens more than once in Marmalade Boy, with the most notorious perpetrators being Kei Tsuchiya (who grabs Miki's medallion/bracelet and gives it to Yuu saying she threw it away; Yuu is Genre Savvy enough to not buy it, but he and Miki still almost break up due to stress.) and Ginny Golding (who lies to Miki by telling her she was Yuu's "other woman" as a prank; this causes the already distraught Miki to break off her and Yuu's Long Distance Relationship.)
Naruto, after finding out that Sakura doesn't care for him at all while he's disguised as Sasuke, is forced to retreat to the restroom because he drank spoiled milk in the morning. While on the toilet, he plans on returning to Sakura, still disguised as Sasuke and acting like a jerk in order to make her hate him. By the time he gets out, though, Sasuke has already escaped his bonds, and coldly told Sakura that he finds her annoying (although the way the scene is presented leads viewers to initially think that it was Naruto in disguise carrying out his plan).
Ranma ½: Ryoga, Shampoo, Ukyo, Kodachi, and other characters all try to sabatoge Ranma and Akane's engagement at some point or other.
Ranma and Akane team up in the manga to thwart the possibility of Hinako and Soun marrying.
At the end of Frank Miller's Daredevil, a grieving Matt Murdock had pressured his rather fragile girlfriend Heather Glenn into agreeing to marry him, which was literally driving her to drink. Believing that no good could come of this for anyone, Matt's partner Foggy and his ex the Black Widow created forged notes telling each partner that the other one wanted to break it off and never see them again. The immediate consequences were never shown, but a few years later Heather committed suicide.
Lana Lang attempted this occasionally when her jealousy of Clark and Lois' marriage got the best of her. In one instance she tried to convince Clark that Lois was a bad wife and left her panties in the Kents' bed in a fit of jealous anger when Clark refused to be swayed by her arguments.
Both Balraj's sister Kiran and Darcy's mother try very hard to keep Jaya and Lalita very far away from Balraj and Darcy in Bride and Prejudice.
Sherlock Holmes went out of his way to try to get Dr. Watson to not get engaged to Mary since he wanted to keep him for himself. He insulted Mary with a deduction and he paid a fortune teller to plant seeds of doubt into Watson's head. He eventually did give his consent.
In Plan B, Bruno's "Plan B" to make his ex-girlfriend Laura and her new boyfriend Pablo break up is to seduce Pablo and drive him away from her. It works, but by then it's not Laura he wants to be with.
In Mulan 2, Mushu tries to break up Mulan and Shang to save his job. When Mulan finds out, she gets pissed.
This is Peggy's plan in The Best Years of Our Lives: she declares that she's going to break up the unhappy marriage between Fred and Marie. It's not really her fault the marriage falls apart, but she does get Fred in the end.
In Pride and Prejudice, Darcy breaks up Jane and Bingley's relationship because he thinks Jane is just stringing his friend along, due to her showing him the same affection she shows everyone (he didn't realize she's just that nice). That he broke them up is the main thing that leads Elisabeth, Jane's sister, to think that Darcy is an a-hole. The reveal of why (caring deeply for and trying to protect his friend) is what leads her to realize that she loves him.
Dr. Austin Sloper in Washington Square goes out of his way to ruin his daughter Catherine and Morris's relationship, culminating in taking her on a trip to Europe for a full year to test the strength of their affection. His reasoning is that he is convinced that Morris is nothing more than a Gold Digger after his family's fortune. He turns out to be right.
Live Action TV
In the sixth season of House, House decides to try to break up Cuddy and Lucas after deciding that he might just be interested in the former.
In Sugar Rush, the efforts of Sugar to sabotage the relationship between Saint and Kim rather indicate that she's not being honest about having no interest in the latter.
On Gossip Girl, this is Blair's MO. And not just for own ex-boyfriends - she's perfectly happy to break up any new relationships that might make Serena unhappy too. Chuck, as well, loves to mess with any relationships that would a) stop Blair being with him or b) distract Nate from their friendship. And Jenny does this occasionally. And Vanessa - oh, screw it, let's just say Gossip Girl is built around this trope and leave it at that, okay?
On How I Met Your Mother Lily has done this to Ted six times, each time because she thinks the girl Ted's dating is a bad fit for their group of friends. Methods range from planting a woman's earring in Ted's bed so his girlfriend thinks he's cheating on her, to planting a Creed CD in the girlfriend's apartment so that Ted becomes disgusted with her, to dressing up in the girlfriend's Darth Vader costume, pretending to be her, and telling Ted they should see other people.
Later on, Lily is called upon to break Barney and Robin up, but a sudden bout of Complexity Addiction almost does her in.
This is pretty much Diana Fowley's job during season six and seven of The X-Files. She's working for the Syndicate to lure Mulder, but whether her true aim in breaking up Mulder and Scully is professional or personal (she's Mulder's ex-partner and may or may not be his ex-wife) is up to interpretation. She plays off Mulder's previous trust in her, and almost succeeds in breaking them up. To the delight of many a shipper, she is killed off in the early parts of season seven.
The season 4 finale of iCarly had a revelation that Sam likes Freddie. It's quite possible that her actions in iSaved Your Life, where she completely fucked up Carly and Freddie's newly formed relationship by planting seeds of doubt in Freddie's mind was a subconscious desire to sabotage the relationship to keep Freddie away from Carly.
In pretty much any episode of Glee in which Finn Hudson is dating somebody not named Rachel Berry, you'll find Rachel trying some form of this, by means including: staging singing lessons that are intended to turn into something a lot less innocent; dramatic changes of appearance (fortunately Kurt was onto her and ensured it didn't work); informing Finn that his girlfriend is pregnant by another boy; duetting with other boys (particularly if it's the boy who got his first girlfriend pregnant) to make Finn jealous; and encouraging him to distrust his girlfriend and spy on the boy a blind item in the school newspaper implies she's cheating with in company with, you guessed it, Rachel Berry. Every single one of these backfires on her in some way. You'd think she'd have caught on by now, but no such luck...
Mary of Downton Abbey tells her sister Edith's suitor that Edith was looking for an "old bore" as revenge for Edith's spreading Mary's Dark Secret.
In Merlin, Morgana tries and fails to break up Gwen and Arthur in "Queen of Hearts" but succeeds masterfully (though temporarily) in "Lancelot du Lac."
In Tokimeki Memorial 2, Knight Templar Big Brother Kaoru "Sou-Banchou" Ichimonji will constantly try to do this in Akane's storyline. Resolved to prevent any boy to hurt her little sister's feelings, and also fearing to lose her (who's his sole family) if she ever hooks with a guy, he will sic at you his underlings, then will fight you in person, will barge in the scene if he feels you're too close from her, and in Memories Ringing On, will even go as far as trying to sabotage your wedding ceremony preparations with her by threatening the assembly hall's clerk of obstruction of business! Said sister is not very pleased by her brother's antics, and constantly resolves them with a Megaton Punch.
Sou-Banchoudoes have somewhat of a point, as his little sister was badly hurt in the past by her first love: a boy who moved away and thus abandoned her when they were little. It really doesn't help that you are said boy, though to be fair it's not like you could do a lot about it.
In General Protection Fault, Trudy steals Ki's stuffed animal "Mr. Pookel" and leaves it where Nick will find it so that he'll learn her screen name. He's upset with her for not telling him in order to test his loyalty, but utlimately forgives her.
Homestuck has a variant skewed a bit by the nature of troll romance. Basically, trolls have four romantic quadrants - "genuine love", "Morality Pet", "mediation between two others" and "mutually destructive hatelust" - and you're generally expected to have relations with a given person confined to only one quadrant. As a result, at one point Casanova Wannabe Eridan attempted to sabotage Feferi and Sollux's "genuine love" romance by trying to make Feferi mediate between himself and Sollux, which would push them out of their preferred quadrant.
The Simpsons once had Bart try to break up the relationship of his Precocious Crush (with the added motivation that the person she was going out with had bullied him).
In an earlier episode, when his best friend Milhouse started 'dating' the new girl at school, he tipped off the girl's Overprotective Dad so Milhouse would hang out with him again. He ended up regretting it.
In another episode, Milhouse's parents (who several seasons back had a nasty Toilet Seat Divorce) are getting back together. Which seems great at first, except that Milhouse starts to feel that they're ignoring him. He complains about this to Bart, and Bart sees a Teen Drama on TV wherein a girl angrily dumps her boyfriend because she found another girl's bra in his room. Bart steals one of Marge's bras and leaves it in the Van Houtens' bedroom. But because the bra had Marge's name sewn into it, it poses a threat to Homer and Marge's marriage as well. Homer and Marge reconcile over the fact that it was a big misunderstanding.
My Dad The Rock Star has Quincy trying to break Willy and Alyssa up because he thinks that if they're together, they wouldn't want him hanging around getting in their way.
Archer tries to get his ex back by manipulating recordings of her current boyfriend in order to make it look like he's cheating on her. She doesn't believe him, but still appreciates the effort.
Archer's mom also purposely drives Lana closer to her boyfriend to get her away from Archer, because while Lana and Cyril are the Official Couple, she can see the Unresolved Sexual Tension between her and her son.
And Archer's "Operation Something About I Rescue Lana and She Begs Me to Take Her Back, so Then Cyril Commits Suicide."
Diaspro in Winx Club is in love with and originally engaged to Prince Sky. However, Sky falls in love with Bloom and breaks up with Diaspro. Diaspro is still in love with Sky and tries to brainwash him with a love potion. When this fails, she turns to more conventional means such as not letting the two spend time together and feeding the two misinformation in an attempt to drive them apart. She's helped when Sky's father declares her his liaison, giving her some power over Sky.