And Now You Must Marry Me

The villain's evil plan isn't always to take over the world or kill the hero. Their goal may be far more personal and sinister: he's going to force the heroine (the love interest of the main hero) to marry him. That depends on the story line.

This whole concept usually carries at least an implicit threat of rape when you think about it. It's an intensely personal threat to the heroine, one that plays up her femininity and vulnerability especially since the marriage is assumed to be permanent and irreversible.

If the heroine has a heroic male Love Interest as she usually does, it serves as a threat to his masculinity as well.

It also provides a convenient excuse for scenes where the villain puts the heroine in compromising positions and it can lead into all sorts of Wedding Tropes. Speak Now or Forever Hold Your Peace is almost mandatory.

Often, the villain is motivated by twisted affection or at least lust, but it can also just be about getting legal access to her money and property or to her title.

On the other hand, he might just be the kind of sick bastard who enjoys the idea of keeping someone trapped in a legally binding relationship that they find repulsive for the rest of their life.

Maybe the heroine herself is pretty much irrelevant, and it's really just about claiming ultimate victory over the hero by stealing his woman.

If the villain does this by kidnapping his desired bride, it's a subtrope of I Have You Now, My Pretty. When combined with Villainous Crush, it's also Abduction Is Love.

If he threatens someone else and offers to relent if the heroine agrees to marry him, that's the G-rated variant of the Scarpia Ultimatum. In cultures with Arranged Marriage, he might convince the heroine's parents or guardians to force her into marriage.

Evil Sorcerers will use their powers to Hypnotize the Princess. The villain might even attempt to trick the heroine into unwittingly doing something that counts as a legally binding wedding.

Female antagonists who use this trope are much less common than male examples, and are usually portrayed a bit differently.

They're almost always motivated by a Villainous Crush (since Villainesses Want Heroes) and may even verge on being a really unstable Abhorrent Admirer rather than an outright villain.

For some reason, female Gold Diggers are more likely to rely on seduction rather than coercion. Their male victims are also much more likely to foil the villainess's plan on their own while female victims almost always have to be rescued by their male love interests.

Examples

 * Jafar tries to force Jasmine to marry him in Aladdin by hypnotizing her father so that he'll set up an Arranged Marriage. It's not entirely clear why he doesn't just Hypnotize the Princess; her father's rather Weak-Willed, and Jasmine is definitely not, so this way might have just been easier. (Even the Sultan does manage to snap out of Jafar's hypnosis on his own at least once.) This example is somewhat unique in that Jafar is really using her as a way to become Sultan. In fact, Jafar's original plan was to simply kill both Jasmine and the Sultan once the marriage had been carried out. Though Jafar was not above creeping on Jasmine after she thought Aladdin was dead and even asks Genie to make her fall in love with him when she was being defiant.
 * In Beauty and the Beast, Gaston uses the Scarpia Ultimatum version on Belle when her father is going to be committed to an insane asylum. It didn't work.
 * The Little Mermaid Ursula in a beautiful form hypnotizes Prince Eric. This is partly to prevent Ariel from fulfilling her bargain of making Eric fall in love with her in three days, and partly out of spite.
 * In The Adventures of Tom Thumb and Thumbelina, the Mole King tries to marry Thumbelina and fails.
 * Didn't make it into the final version of the film, but this trope was very heavy in one scene that was cut from The Lion King. Scar was going to attempt to force Nala to marry him. Later, a similar scene found its way into the Broadway version.
 * The evil penguin Drake from The Pebble and the Penguin demands that Marina choose him as a husband during the mating ritual, or go to a watery grave ("Right this way to the Drake estate / or write your epitaph!")
 * The Swan Princess: The villain Rothbart once tried to take Odette's kingdom by force, but it didn't work out so well. So he kidnaps Odette and turns her into a swan every time the moon sets until she agrees to marry him and give him a legal claim to the throne. That doesn't really go his way either.
 * Beetlejuice: The title ghost's ultimate goal is to marry teenaged Lydia (a move that has Squick written all over it), because this will apparently allow him to stay in the world of the living indefinitely.
 * In the Super Mario series, Bowser's schemes, more often than not, were made to forcibly marry Princess Peach, both to consummate his control over the Mushroom Kingdom and to be with his Villainous Crush.