A character is trapped in an Arranged Marriage with someone they don't love at all. Their parents are dead set on them marrying this person, so they can't talk their way out of it, and they certainly can't stand to go through with it, so what's left for them to do? Running away, of course.
This is a common pastime for the Rebellious Princess. If a character waits until after the wedding ceremony has begun to do this, she's a Runaway Bride.
In the anime Cosmic Baton Girl Comet San, the main character considers running away from a party where a prince will be betrothed either to her or her rival, only to find that the prince beat her to it by running away himself.
In Pokémon, it is eventually revealed that James of Team Rocket ran away from home to escape marriage to the insane and sadistic Jessiebelle. While he did have feelings for her at one point, he loved his Growlie (his only friend, a pet Growlithe) even more, and her attempt to get the dog out of the equation was the breaking point.
In Rune Soldier Louie, Melissa ran away from arranged marriage and even became a priestess to Mylee, the God of War to make sure her parents couldn't force her back.
In the very beginning (first episode/volume) of Ranma 1/2, it initially looks like Ranma Saotome might become this to Akane Tendo, given that he's expressed no interest in her and openly stated that he considers finding a cure far more important than getting a girlfriend. Of course, his (currently her) plans to leave are curtailed when Akane knocks him/her out cold with a table for insulting Akane's (lack of) figure compared to his/her cursed form. When Ranma comes around, he first gets enrolled in school, then caught up in the chaos, so he forgets all about it. One Alternate Character Interpretation of Shampoo could place her as this, using chasing the Saotomes as an excuse to get away from Mousse (though he isn't actually engaged to her and she has no interest in him). By the end of the manga, Ryoga Hibiki is something of an unwilling version of this trope- he wants to be around his newfound (and borderline Relationship Sue) love interest Akari, but his lack of direction means he can rarely even find her.
In Romeo X Juliet Romeo is arranged to marry Hermionine, he falls for Juliet and they run away together. Unfortunately for them, they get caught.
This is part of Kyrie's back story in Umineko no Naku Koro ni. She ran away from the arranged marriage to marry the protagonist Battler's father, Rudolf. It should be noted that she'd been in a relationship with Rudolf for awhile, even when he was married to Battler's mother, Asumu (Or not). Unfortunately, This resulted in her younger sister Kasumi being forced to marry the fiance. Having already promised herself to someone else, she's pretty miffed about that. And considering how Kyrie dies on Rokkenjima, the grudge is transferred to Kyrie's daughter, Ange.
Clarice in Lupin IIIThe Castle Of Cagliostro bailed when the guards left her room to allow her to change into her wedding dress (presumably to rehearse the ceremony). But in spite of Lupin's efforts, she was recaptured, and this time imprisoned in a tall tower. One that could only be entered via a retracting bridge or a hatch on the roof. Other features included grenade-proof glass.
Jenny Doolittle does this in Bodacious Space Pirates, shooting her way out before stealing a brand-new stealth fighter, then hires the eponymous pirates as her escort. Her answer to family pressure seems to be More Dakka. Too bad her family has their own fleet.
Prince Akeem (Eddie Murphy's character) in Coming to America convinced his father to send him to America as a sort of extended bachelor party, when in reality, he was looking to escape his arranged marriage and find true love.
Just before the ceremony is to start in the movie Arthur, the title character and his lover Linda go to his fiancee Susan to tell her the wedding's off. Susan's father tries to kill the lovers and is only stopped by Arthur's grandmother - but he does beat Arthur up enough that he's black and blue when he explains to the guests what's happened and then passes out on the altar.
In the 1991 film version of Robin Hood, Maid Marion (Uma Thurman) runs away to Sherwood Forest to escape her arranged marriage to Sir Miles Flaconet (Jürgen Prochnow).
In Titanic Rose DeWitt Bukater fakes her death in the Titanic disaster and changes her name to escape her engagement. Before the ship went down she told her intended that she's rather be Jack's whore than Cal's wife. Before that she wanted to kill herself so she didn't have to marry him.
In the live-action Disney film The Sword And The Rose, Princess Mary Tudor (sister of Henry VIII) unsuccessfully attempts to run away with Charles Brandon rather than be married to the aging King of France. It should be noted that the film is historically inaccurate; the real Princess Mary did in fact elope with Brandon, but not until after she had married King Louis and nursed him through his final illness.
Fanfan la Tulipe in the 2003 French movie of the same name. He is a 18th century libertine and doesn't want to be involved in a relationship of any kind. He is caught up teaching a lesson to a young woman inside a haystack and her father forces him to marry her. He escapes the wedding ceremony and engages in the French army.
Talia, the main character of the original Heralds of Valdemar trilogy, does this, although she left before being assigned a specific bridegroom. She was thirteen at the time.
Kethry from the related Vows and Honor duology was a year or two younger when her old nurse smuggled her from the home of the new husband her brother found for her. Unfortunately it was after the marriage and consummation of same.
Princess Cimorene in Patricia C. Wrede's Dealing With Dragons. Her parents try to con her into marrying the empty-headed prince of a neighbouring kingdom, so, on the advice of a talking frog (it happens in a fairy-tale universe, after all), she decides to run away.
The Corinthian has Pen running away from marriage to her cousin, and then helping another girl run away from a proposed marriage to her.
Bath Tangle actually has a subversion, of sorts: the hero's unwanted fiancée runs away from him...and then is persuaded to go back by the heroine, who argues that a loveless but comfortable marriage to the hero (who isn't nearly as horrible as he seems) is much better than a hasty elopement with the hero's poorer nephew.
Kitty in Cotillion is a slight variation - her guardian is forcing her to marry one of his many nephews (but it's her choice which), so she runs away. And then subverted, in that she meets one of the nephews in the local inn five minutes later and comes up with a better plan.
In The Frog Princess by E. D. Baker, Emma runs to the swamp when she finds out she's to be engaged to an empty-headed and vain prince. She didn't intend to stay for long, but she ended up turning into a frog. Yeah, another fairy-tale universe.
Subverted in Shabanu, where the title character tries to run away from an arranged marriage to someone old enough to be her grandfather. She gets (severely?) beaten up by her parents, and marries the guy anyway.
Averted in Soul Music, where the troll princess Jade says she'll refuse to wed the prince her parents have chosen for her, and that she'll run away if she has to. Susan persuades her to at least meet the potential groom first: he might turn out to be nice.
Frederica Vernon of Jane Austen's Lady Susan runs away from Boarding School when she finds out her mother, the titular Lady Susan, intends to force her to marry the ditzy Sir James Morton against her will. She gets caught on the road.
A Song of Ice and Fire: No one's a hundred percent clear on the events surrounding Rhaegar and Lyanna, but one version - the nicest version - is that she abandoned her betrothal to Robert to be with him.
An episode of the 1980s series Beauty and the Beast (nothing to do with the Fairy Tale or Disney movie) has Catherine and Vincent helping a young Chinese woman escape an arranged marriage. Unfortunately, the man she was to marry was the son of a high-ranking member of a Triad which knew all about the World Below.
The F Troop episode "From Karate With Love", which focused on a runaway Japanese bride and the Samurai sent to fetch her.
Princess Seraphine in Puzzle Quest, an optional party member. Kinda understandable since her calculating father wanted to marry her with a tribe of barbarians to stop them from raiding his kingdom. Also, his poor treatment of the player character just asks you to interfere. However, since she's optional, it's also perfectly possible that she gets married if the player doesn't help her.
Millay of Suikoden IV fled Middleport when Schtoltenheim Reinbach II planned to make her marry his son. Her parents approved the marriage; she didn't, so she made a break for it. Your hero happens to meet her just as Reinbach II's goons track her down — ironically enough, this is also the first time Schtoltenheim ReinbachIII meets her, and he's blissfully unaware of the situation until after they've helped her out. Then he's completely horrified at his father's terrible deeds, and apologizes profusely.
Hilgya's backstory in The Order of the Stick is one of these, though she's more of a runaway wife than fiancee. The catch? Her husband was kind, loving, and supportive, but Hilgya acted as though he was oppressing and belittling her.
Girl Genius: When Agatha is first acquainted with Sleipnir O'Hara, Sleipnir mentions that she has an arranged marriage waiting for her at home. In the next arc she shows up in, she's with Theo DuMedd, but at first it's impossible to tell if they're in a relationship or just close friends. She's definitely run away with him.