Usually female, this character's sole purpose in the story is to misunderstand, obstruct and otherwise torment the male hero, thus creating unnecessary complications of plot until the end, where she finally rewards the hero with her hand or other body parts.
This character trope is Older Than Print, dating back to the unreasonable lady-love of medieval romances. An especially irritating version is often seen in war movies or action films, whining about being "neglected" when her significant other is absorbed in vital, world-saving projects.
It's worth noting that when Akane isn't making Ranma's life more difficult, she's actively working to help him without demanding marriage in return. Which is part of the reason he really could do worse than her. Also, Ranma himself also makes her life difficult, just in a different and less appreciated way.
There are also two one-sided examples with Belarus and Russia and Belarus and Lithuania. Belarus stalks and terrifying her brother, certain she can get him to marry her, but her being his love interest is all in her head. Meanwhile, Lithuania sees Belarus as a love interest, while she's not interested but still breaks his fingers while on a date. Subverted with Hungary, who beat up her future husband Austria before she became his love interest.
Played straight and depending on if you think it's funny, parodied in the yaoi title Ill Be Your Slave. The Obstructive Love Interest is a pretty boy, well aware of his looks, who's used to having his admirers doing everything for him. The seme becomes his dedicated slave to keep him co-operative in a modelling job. The boy abuses this to no end.
In the film of Stardust, Victoria Forrester is a big one of these. Of course, we're not meant to like her, and even The Hero comes round eventually. In the original book, she's a lot more sympathetic, mainly because she seemed to make her claim sarcastically and didn't actually expect the Hero to try to fulfill it, feeling guilty when he does.
Jocelyn is this to William in A Knight's Tale. Among other things, she has him lose battles intentionally (since any knight ever smitten by her good looks has tried to dedicate his victory to her, she asks for William to demonstrate his love by going against his own nature and losing for her instead), then after he goes through with it long enough to be almost knocked out of that tournament, she asks that he win all the battles left just to prove his love.
Mary Jane is the whining variant in Spider-Man 2, with all her screentime devoted to Peter pining over her or her pining over Peter without much to add for herself.
In the sequel, this is actually reversed and Peter becomes the obstructionist toward Mary Jane's character arc.
Chev's girlfriend in Crank isn't the sharpest tool in the shed and can't comprehend the gravity of the situation Chev is in.
Vicki Vale was more or less this in the 1989 Batman film.
Gordon R. Dickson seems to have a weakness for this trope. In the Childe Cycle, both Anea Marlivana from Dorsai and Melissa Khan from Tactics of Mistake are obstructive love interests in spades. (The latter is lampshaded in the later story "Amanda Morgan", where the title character observes that Melissa is terrific in a crisis, but incompetent the rest of the time.)
On the other claw, while Angie Eckert was a Distressed Damsel in Dickson's The Dragon And The George, through the rest of the Dragon Knight series, she is a supportive, capable, competent ally of her husband.
Male version: Walter on Ugly Betty (actually, it seems that all of Betty's boyfriends will turn into this if they're around long enough).
The love interest in Unfit exists entirely to make unreasonable demands for the main character to deal with. She is never in the right, she never shows any positive emotions towards the main character, and it's impossible to tell why he hasn't dumped her yet. In contrast, he's always a perfect saint towards her. (One can't help but suspect that the author had a failed relationship and is using the comic to work through his own issues.)
Metal Gear Solid 2's Rosemary. OH GOD, Rosemary. Raiden is off trying to save the world (or, at least, save the President of the United States and his entourage from a superpowered black-ops cell gone rogue, and with access to nuclear weapons) and all Rose can talk about is how he refuses to discuss their relationship and how his room in his home contains nothing but a desk and a bed. Poor Raiden can only sigh and try to insist that they'll talk about it after the mission, but she won't let up. And creator Hideo Kojima supposedly based her on his wife.
Subverted? Played with? Who knows with MGS2, but the REAL story is: Rose is intentionally screwing with his feelings under orders from the Patriots, in order to make sure the S3 training project can sufficiently compensate for personal emotional stress. This goes so far that Raiden is taunted by an AI copy of Rose during the final sequence of the game just to twist the knife into his psyche further.
Princess Zelda, in the animated The Legend of Zelda, drove Link absolutely crazy with this sort of behavior. And the poor guy never DID get the kiss he was always hoping to win.