Damsel In Distress: Live-Action Films aka: Live-Action Films
The Ur Example of this in film would probably be the protagonist of the 1914 silent melodrama serial The Perils of Pauline. A "talkie" version of the series was made in the '30s; the title was later used for a 1947 biopic of original Pauline actress Pearl White, and a 1967 film that was a camp spoof of the genre.
Pearl White also starred in a nearly-identical series, The Exploits of Elaine, around the same time.
Thunderball. Bond's fellow agent Paula is kidnapped by a couple of Largo's thugs and taken to be tortured for information. Bond goes to Largo's estate to rescue her but arrives too late. Paula has taken a Cyanide Pill and killed herself so she can't be made to betray Bond and the operation.
Ditto for Elizabeth Swann in the first Pirates of the Caribbean, except the feminist-friendly parts were added by the actress herself. Said actress gets a much more fitting role in the sequels.
Played straight and then subverted as said damsel takes a level in badass over the course of the movies. It gets lampshaded by Jack when he refers to her as "a certain damsel in distress... Or should I say distressing damsel." after her Shoot the Dog moment of leaving Jack to die.
If Elizabeth is this in the first movie, then Will must be as well, because he ends up having to be rescued from the exact same situation. She manages to instigate his rescue despite being marooned on a deserted island, and then actively fights alongside him in the final battle.
In the Spider-Man Trilogy, Mary Jane gets kidnapped by the villain in the climax of all three movies. She's also in distress twice before the climax of the first.
Done remarkably effectively in Superman (1978) - the famous helicopter rescue, but all of the climaxes in the movie involve this trope. Also used in the sequels.
Played fairly straight in 'Sync' episode 6, where computer prodigy Yoshi appears to have no sense of fighting or quick reasoning skill whatsoever. Ruthlessly exploited by our 'Genre Savvy' main character when he gets her to panic in his favor by suddenly yelling, "Oh god, look at all the bad guys coming to get you, get on the motocrcycle, quick, they're right behind us!'
Aversion: In The Proposition, this role is occupied by the retarded younger brother. Obviously, there is no Rescue Romance. At the end, however, Charlie still has to rescue the police captain's wife from being raped and killed, although the captain himself - despite being Ray Winstone - is also being threatened, though not with rape.
Subverted in Ever After: when Danielle is sold into slavery, Prince Henry shows up to rescue her. But, being the capable heroine she is, she has already threatened the bad guy and freed herself.
Marion Ravenwood in Raiders of the Lost Ark. She's captured by Todt and threatened with torture in her own bar and has to be rescued by Indy. Later in Cairo she's captured by the Germans' Arab allies and carried away in a basket. Then she's captured yet again by Nazi troops while she's aboard the ship. Somewhat averted because she isn't completely helpless, including knocking out one of her Arab pursuers with a frying pan and pulling a knife on Belloq in an attempt to escape.
Subverted at the end of Indiana Jones and the Last Crusade. Elsa became a distressed damsel when she found herself dangling over a crevasse after she tried taking the Holy Grail from its resting place. However, rather than letting Indiana pull her up to safety, she uses his hold to try and reach for the chalice, which had conveniently fallen just below her. In the final moment, she almost reaches the grail until her hand slips away from Indy's, causing her to suffer a Death by Materialism.
Hey, she did manage to trick Darkness into believing her Face-Heel Turn long enough for her to free the unicorn. She got knocked out immediately afterwards.
Giselle starts out like this in Enchanted but reverses roles with Robert in the end.
Princess Leia from Star Wars manages to be this and simultaneously an Action Girl. However she is something of a subversion because her plea for help was not a plea for a rescue but rather a plea to get the plans to the Death Star to Bail Organa on Alderaan. She wasn't expecting a rescue at all (and the guys didn't plan to do it either).
And she wasn't exactly what one would call grateful when she did get the rescue, either.
Princess Leia: I don't know who you are or where you've come from, but from now on you'll do as I say, okay?
Carrie Fisher herself said: "I was not a damsel in distress. I was a distressed damsel."
Rather funnily, Han Solo, of all people, plays this role in Return of the Jedi. He is rescued from a dragon... by a princess. And he is helpless and weak when she rescues him, seeing as he's blind at the time. This doesn't prevent him from (accidentally) knocking Boba Fett into the Sarlacc Pit - and then rescuing best friend Lando Calrissian after Lando had come to rescue him!
If Jabba has her as his slave girl, in the end she's the one who kills him.
In Hudson Hawk, a kidnapped Andie MacDowell pretends to suffer side effects from curare poisoning so she can annoy the typewriter symbols out of her captors and lampshade the trope: "I'm not a very good damsel in a dress, am I?"
Averted in Iron Man 1. Pepper Potts has to be rescued, but is enough of a threat that the villain feels compelled to shoot her instead of taking her hostage. She's also generally competent and helpful throughout the film.
Indeed, the one scene that seems obviously headed for her being captured and turned into a distressed damsel has her instead easily evading the villain's clutches, and then immediately alerting the authorities to his evil plans.
Done again in the sequel, when Happy Hogan insists on accompanying S.H.I.E.L.D Agent Romanov on her mission and fights a bad guy when they enter the building. By the time he has won the fight, he sees that she's taken down every other bad guy there is.
And shown again with Miss Romanov in the beginning of The Avengers. She's held captive by a group of Russian mobsters who are ready to kill her until Agent Coulson calls her, ready to bring her back in. She easily frees herself and drops everyone she was dealing with in no time flat. With Coulson listening in on the whole thing.
In X-Men, Rogue is kidnapped by Magneto for his machine.
Double subverted in True Grit western: the main character is a 14-year old girl trying to prove her companions she doesn't need babysitting, and succeeding. However, eventually she does, in a perfectly classical way: first getting kidnapped by outlaws, than falling into a snake pit.
Subverted in The Avengers (1998). Emma Peel is captured by Sir August and brainwashed into a hallucinatory state. You'd expect Steed to break in and rescue her, but instead she escapes from Sir August, fights off her delusions and breaks out to freedom by herself.
In Perfume, the Villain Protagonist sets his murderous sights on Laura Richis, a beautiful, virginal young lady. Her father becomes wary of the danger and does everything in his power to protect his daughter.
Tank Girl. Sam (a 10-year-old girl) is captured several times, with Tank Girl spending the movie tracking her down in order to save her. Subverted at one point when Sam cleverly uses a deadly toy to puncture a child molester's hand.
Sam: That's what you get for being a perv!
Tina (Cameron Diaz) in The Mask. Although she is able to get Dorian to take off the mask and then kick it to Stanley, which leads to the battle being won.
Cliffhanger. Jessie Deighan turns into one. She's a helicopter pilot. She does mountain rescues. Then she gets scared by bats in a cave, and cringes in a corner while the he-men fight.
Subverted hilariously in a scene of The Boondock Saints II All Saints Day with Agent Eunice Bloom. She's snatched into an impenetrable panic room by a baddie (right in front of the cops, no less), and pandemonium breaks out. One of the cops even worries that she might be "touched and stuff", and it's played as high drama for a bit. He needn't have worried; in the next shot, Special Agent Bloom has the baddie pinned down and sputtering for relief.
Wild Wild West. Rita Escobar, whose husband was kidnapped by Dr. Loveless and who ends up getting imprisoned and kidnapped by Loveless herself.
Played straight in The Princess Bride. Princess Buttercup gets kidnapped by Vizzini, nearly eaten by the shrieking eels, is the oblivious target of a murder plot, gets set on fire, falls into a sand trap, and nearly gets maimed by a rodent of unusual size. At one point she even contemplates taking her own life.
Subverted with Kelly in Mystery Team. Yes, she DOES get kidnapped... but it's not like the Mystery Team were much help in saving her.
Reconstructed in the Scooby-Doo movie. They point out that while, yes, Daphne did get kidnapped a lot, she never let that discourage her from joining the gang in their latest mystery. She's also Genre Savvy enough to have studied martial arts so that she is eventually able to look after herself.
Daphne: (after defeating a henchman who tried to kidnap her) Now who's the damsel in distress? Henchman: Me? Daphne: Straight up!