In what's probably a nod to the original show, Face is captured by bad guys and tied up in tires while wearing nothing but an open bathrobe.
Also Hannibal at the very beginning of the movie, getting punched by two corrupt Mexican cops while handcuffed. Unfortunately for their boss, they're dumb enough to leave him alive. This ends badly for them.
Back to God's Country: Peter gets his skull cracked when Rydal, the villain, drops a ship's boom on him in a Make It Look Like an Accident stunt. That puts him out of commission for the last act of the film, so it's Dolores—the heroine, and the woman Rydal would like to rape—who has to get a gun, hijack a sled and dogsled team, and get herself and Peter to safety.
Barbarella: Pygar the angel is extremely ill-equipped to deal with the evil and insanity of the city of Sogo, leading to Barbarella having to save him a couple of times; from a group of Sogoites who want to shred his wings and stab him with a scythe, and from the Black Queen who holds him hostage and crucifies him.
Moore in Big Game, when he's locked in a refrigerator hanging under a helicopter and about to be carried away for seven days of torture and painful death. Cue Big Damn Heroes from Oskari.
This happens to a wounded Hannibal King in Blade: Trinity when he gets captured by vampires.
Cirque du Soleil: Worlds Away: After falling into the Cirque world, the Aerialist is captured by the Archers and Spearmen from KÀ and taken to the Counselor.
In Dad's Army (1971), three Nazis parachute into Walmington-on-Sea and hold everyone at the church hall meeting hostage, including the Mayor, The Vicar, and the Verger.
This happens to the character of Kale in the movie Disturbia, and his Love Interest Ashley rescues him.
The Scaled Up antagonist of Enchanted intends to grab the female lead as a Damsel in Distress, but the male lead makes the mistake of proclaiming that this will happen "over my dead body." The resultant Gender Flip does not go without lampshading.
Fire with Fire: Jeremy is beaten up multiple times and nearly killed. Near the end Talia comes to save him from Hagan before he's killed.
Harrison Ford spent a good chunk of his early career being kidnapped, tied up, and/or tortured:
In GoldenEye, Alec Trevelyan holds Bond at gunpoint and threatens to shoot him if Natalya doesn't undo her sabotage of the GoldenEye satellite. Natalya coolly replies "Kill him. He means nothing to me." Bond silently but wearily accepts the point.
In The World Is Not Enough, Bond gets put into a torture machine that slowly strangles him and will break his neck if pulled far enough.
Bond is captured by the North Koreans in Die Another Day and spends the title sequence being beaten and tortured.
Spectre has Bond tied to a chair while holes are drilled into his head.
"Joy Ride 2: Dead Ahead" is exactly this trope. When the character of Bobby is kidnapped by Rusty Nails, his fiance Melissa must save him. Later on, the other male protagonist is kidnapped.
In Kick-Ass, Dave and Big Daddy get tortured on streaming video, before Hit Girl arrives to stop the show.
Funnily enough, before that, in the first two Iron Man films, both Tony and Rhodey act like this at different points. In Iron Man, Tony is captured at the beginning by the terrorist group The Ten Rings, and forced to make a missile for them; it's this capture, combined with giving him access to a box of scraps, which leads to him building the Iron Man armor in the first place. Later, the villain Obidiah Stane catches Tony by surprise in his home and takes out his Arc Reactor, which Tony now needs to live, putting him into Cardiac Arrest until he can get to his older, less powerful Arc Reactor. In Iron Man 2, Rhodey, now using the War Machine armor, has his armor hacked by Ivan Vanko and is trapped inside the armor as it attacks Tony, putting him in danger until Black Widow can re-hack it and free him.
In The Avengers, Hawkeye's primary use in the film is to motivate Black Widow, his partner in the field, to rescue him as he's been captured by Loki and used as a Brainwashed and Crazy weapon, leading to her helping to form the Avengers. Due to the nature of how he's been captured, she basically ends up saving him from himself through an "I Know You're in There Somewhere" Fight, and once rescued and given time to recover, Hawkeye helps the others in the final fight, which allows them to save the other Distressed Dude, Selvig.
Iron Man 3, though Pepper is the one who spends most of the film in danger, and thus is a Damsel in Distress, Tony's pal Rhodey is also briefly captured by AIM, who pry off his armor and use it as part of a plan (though, had it not been for their Extremis powers, they'd have probably had difficulty holding him as see by his brief escape attempt). Said plan, funnily enough, involves capturing the President and executing him live, forcing Tony and Rhodey to work together to save him, making him another example.
In Captain America: The Winter Soldier, Steve realizes halfway through the film that the title villain is none other than Bucky, brainwashed and used as a living weapon by HYDRA; and thus, he goes through a similar experience as Widow went through in Avengers.
Thor when he is beaten by Thanos and left floating in space, injured and unconscious. Just ask Star-Lord:
Tony Stark: You know Thor? Peter Quill: Yeah, tall guy, not that good-looking, needed saving.
Doctor Strange gets kidnapped and tortured by Ebony Maw in an attempt to steal the Time Stone from him, and has to be rescued by Iron Man and Spider-Man.
After Vision is badly injured, multiple heroes try to save him from being captured and killed by Children of Thanos. In the end, Thanos kills him anyway.
In the first Matrix movie, Agent Smith and a few other agents ambushed Morpheus's crew in an old building. The rest of the crew (except for the dearly departed Mouse) escape, but Morpheus was abducted. With him in his custody, Agent Smith attempted to interrogate him into giving them the codes to get into Zion's mainframe. Luckily, Neo and Trinity were on their way to rescue him.
Likewise, Neo was apprehended by agents on multiple occasions, such as the scene in first film where a tracking bug is placed in his belly button.
Happens at the end of Mission: Impossible III, after Tom Cruise's character electrocutes himself to short out the bomb in his head (yes, really), the Love Interest he just rescued has to revive him, but before doing so has to take out the Big Bad and his mooks all by her lonesome while the hero lies prone and unconscious.
One of the scripts that the girl from the South Korean movie My Sassy Girl shows to Gyeon-Woo is of a female action hero traveling back in time to rescue her lover, who has been captured by the enemy.
The eponymous Mystery Team has this happen to them a lot.
The first three Pirates of the Caribbean films share the In Distress role around a bit between the original 3 leads — Elizabeth gets more time in it than anyone else, true, but the other two get it sometimes, and as they're both male...
Steve in the opening to the first Scream is an extreme example.
In Alfred Hitchcock film Stage Fright (1950), Jonathan is a fugitive suspected of murder, in desperate need of help. His ex-girlfriend Eve shelters him and sets out to prove his innocence.
Supergirl: Ethan finds himself in several dicey situations requiring his rescue by the Maiden of Might.
Turbo: A Power Rangers Movie gives double trouble with a damsel & a dude in distress(Kimberly & Jason). Not to mention Bulk & Skull.
In Valerie and Her Week of Wonders, Valerie rescues her brother Eagle first from being chained in the town square, and then from being handcuffed in the middle of a river.
When Taekwondo Strikes: When Li is taken prisoner by the Bansan Karate School, Japanese spies beat him, whip him, and burn him with a brand. His students must rescue him.
Wonder Woman: We first meet Steve trapped in his sinking plane, rescued at the last second by Diana. Then she has to save him a second time from her own people. It happens a third time in London when German soldiers try to steal back something he stole on his earlier mission. He's not useless in the slightest, but, yes, he needs a lot of saving.
Charles Xavier is put through what could be considered an even worse hell in X-Men: Apocalypse compared to the two previous films in the rebooted series. When Apocalypse manages to connect to him via Cerebro (only because Charles was appealing to Erik and didn't realise he was there) in order to set off the entire world's nuclear missiles, his great awe at Charles's mutant powers instantly turns into kidnapping and near-successful possession of his body in his need to transfer his consciousness to him since Charles's powerful telepathic abilities would enable him to have access to everyone on the planet. Even a fight on the astral plane leaves Charles battered and bloodied due to Apocalypse's No-Holds-Barred Beatdown of him, at which point he calls on Jean to unleash the Phoenix Force to disintegrate the god-like mutant.
Despite being an extremely competent gunslinger, the Pecos Kid spends much of Yellow Hair and the Fortress of Gold getting himself into scrapes and having to be rescued by Yellow Hair.
