Everybody is Distressed sooner or later. There's even episodes where Buffy takes this role. In the first few seasons, Willow is the main Distressed Damsel. In second two, she and Xander share the role. As Willow grows in power in seasons three and four, Xander, Giles, and Spike end up in this position more often than the others. In seasons 5 and 6, it's Dawn. In season 7, it's the potentials.
Buffy: Dawn's in trouble. Must be Tuesday.
Buffy was this in the Season 2 episode Halloween, when an enchanted costume causes her to become a very helpless 18th century noblewoman.
Subverted by the show itself, however, as Buffy appears to be the stereotypical petite, blonde girl who is constantly in need of rescue, which she almost never is and on the rare times that she is captured, she almost always gets herself out of trouble.
Also the Season Three episode "Choices" plays with this trope as Willow gets captured by The Mayor and does eventually need rescuing but only because her attempts to liberate herself fell through when she got distracted gathering intelligence about The Mayor's plan which was arguably good trade off since she knew Buffy would get her out anyway.
Cordelia was this when she was on the show. Not so much after she moved to Angel.
Anne was this twice. She appears again on Angel, a good deal tougher.
Wesley: You have to lie down. Fred: I am not — I am not the damsel in distress. I am not some case. I have to work this. I lived in a cave for 5 years in a world where they killed my kind like cattle. I am not going to be cut down by some monster flu. I am better than that!
LazyTown sometimes has Stephanie being kidnapped by the "evil dude".
In Firefly, it seems that every episode that centers on River has her in serious danger, needing some Big Damn Heroes to save the day...except for "Objects in Space," where she hits the villain with a plan.
The ironic part is that by Serenity, she's activated hidden Waif-Fu powers that would have let her handily deal with every one of the bad guys gunning for her in the series.
River in the series got so smart and powerful that Serenity's own crew starts to worry about whether she's safe to keep around.
It makes sense, given that Serenity was used to tie up loose ends in the story. Given how "Objects in Space" went, it seems that the next season would have had River slowly regain her former fierce intellect and use it far more often.
She showed some signs of her impending badassery earlier on in the episode "War Stories" when she gunned down three of Niska's men with her eyes closed in order to save Kaylee, who would have shared Distressed Damsel duty had the series actually continued. Joss Whedon has said something to the tune of, "Whenever we wanted to up the suspense, we just put the cute engineer in danger."
And it's been similarly commented that anytime a man infiltrates the ship he does so by befriending Kaylee, flirting with her and then threatening her at gunpoint. (This happens twice, with Simon in the pilot and then Tracy in "The Message", and probably would've been a continuing trend.)
Lana Lang in Smallville. The whole first season was one big Lana capture-fest. And most of the second. Usually by kryptonite mutants who ''loved'' her. And once they had her, they often tried to kill her, for no better reason than to give Clark a chance to arrive JUST IN TIME! One later-season character actually commented sardonically to his obsessed stalkermutant friend "Lana Lang? Gee, how original."
Subverted with Chloe Sullivan. While she needs to be rescued now and then, as Clark puts it himself, she saved him more times than he could have ever saved her.
Subverted with Lois Lane in more recent episodes; while she tends to need rescuing on a semi-regular basis, she often ends up saving her own skin, and will never be defined as "helpless". She also lampshaded this trope in the Season 10 episode "Harvest", when she ended up getting kidnapped by a rural community who wanted to sacrifice her in a harvest ritual, after wanting to prove to Clark that she didn't need protecting:
"I promise to eat a heaping helping of crow when we get back home, but right now, do your super-speedy thing because this fair lady needs some rescuing big time."
Gossip Girl does it at least once per season, when characters put aside their problems to help Serena: in season 1, when the Nate/Blair/Chuck love triangle takes second place to Serena's confession that she (allegedly) killed somebody; in season 2, when again the aforementioned love triangle is paused when the three characters try to get her out of jail, and in season 3 when all pending matters (Chuck's grief over his father's death anniversary, Lily's postponed confession to Rufus about a night with her ex-husband, Eric's and Jenny's constant fighting, Dan's lingering feelings for Vanessa) are frozen (and then solved or exposed, one by one) when she's on a car accident and over half of the cast go to the hospital to be with her.
The game show version of The Perils Of Penelope Pitstop has Penelope in distress in the same manner as the cartoon where H.C. wants her dead, missing & never found, etc.
Often done in Scrubs about a patient's dying or miraculously recovering ending bickering about less important matters.
One episode turns the plot of that episode into a medieval fantasy. In it, the patient becomes a damsel in distress that everyone works together to save.
In Power Rangers in Space, just try to count how many times the Rangers themselves get tied up, to either figure a way out in time for the big fight, or be rescued by the one Ranger who wasn't there at the time.
How many other times did the Power Rangers have a damsel in distress?
Supernatural tends to apply this trope so much it gets annoying after a while. The Victim Of The Week (usually female) is either being threatened and can't help herself out or Sam is pinned to something and helpless against the MOTW or Dean is doing something stupid/going off on his own, getting nabbed and needing Sam to save his arse.
They've subverted it twice with Sam, though. In Bloodlust, the vampires capture him but let him go after they've given him a good talking to and in The Benders, he manages to get out of his cage without Dean's help and Dean ends up being the tied up one in need of saving.
Farscape put every character, male and female, hero and villain, into such a situation—notably John, who is captured and tortured at the end of the first season and is rescued by Aeryn (with help), and Aeryn, who is captured and tortured at the end of the final season and is rescued by John (with help). This makes sense, as she is the Action Girl at the start of the show, and while he's not quite an action hero by the end he has gotten badass enough to return the favor.
Subverted (a bit) in Doctor Who (notorious for women who needed rescuing from bug-eyed monsters at every cliffhanger) with Jo Grant (UNIT assistant to the Pertwee Doctor) who was a trained spy/escapologist, and thus was the one who freed the Doctor when they were captured. (Lampshaded also by Sarah Jane Smith when she rescues the Doctor from a cell in The Android Invasion and quips: "This time I'm saving you!" She'd also done it in the first episode she was in, The Time Warrior.) Jo Grant was originally conceived as an Emma Peel-typeAction Girl but they cast Katy Manning after her somewhat ditzy audition, a classic example of the difference between what the producers say they want and what they actually want.
Barbara Wright alternately played this trope straight and subverted it. The most memorable straight example would be in the very first Who serial An Unearthly Child, where she spends most of the last two episodes screaming and crying. She seems to have gotten it out of her system by the next serial, where she's perfectly happy to go on a commando raid into the Dalek city. Her most memorable subversion is probably The Crusade, where she does get kidnapped, but rescues herself and is on her way back to rescue everyone else by the time Ian shows up to save her.
Mary Tamm was initially leery of taking a companion role in the series for this very reason, but she was assured that her character, Romana, would be an intellectual equal to the Doctor and a competent woman to boot. Supposedly, she left the role later on because she felt it had reverted to this trope (although possibly she left because she was having a baby — the internet is not very clear on the matter.)
Lampshaded in the new series episode "The Empty Child", when the Doctor learned that Rose was hanging from a barrage balloon during a Nazi Blitz attack. "I've travelled with a number of people, but you're setting new standards for being peril-friendly."
On a whole, the companions in the new series seem to swing between playing this trope straight and subverting it. In the event that the companions are captured and can't save themselves, they at least try to, or find information, or help the Doctor, or at least sass their captors.
It at least makes sense why this would happen. To create tension you need someone to be captured, and since the Doctor's companions are 90% female, it unfortunately becomes this trope.
In The Krotons, Vara — and later Zoe, when she too is chosen for a "companion".
Think what you will about Stephen Moffat but River Song almost never needs rescuing. The few times she does it's typically because she's flung herself off of a building or into the vacuum of space in an attempt to evade capture, specifically because she knows The Doctor will come show up in his handy time machine.
Parodied in the Captain Proton holoprogram in Star Trek: Voyager with secretary Constance Goodheart, whose only function is to be captured by the villainous Dr Chaotica so Captain Proton can rescue her, and whose only dialogue is an ear-splitting scream. When Seven of Nine is roped in to play Constance she asks what her function is. Tom Paris (playing Proton) replies awkwardly that her job is to "tag along on all the missions".
Topanga plays with this trope in the second season's Halloween episode of Boy Meets World:
Cory:(seeing Topanga in a long gauzy dress) Why'd you have to wear that? Topanga: I'm a damsel. But not the distressed kind, one who's totally calm and in complete control of her own destiny.
The X-Files: Gillian Anderson may consider Scully to be a good feminine role model, but there's no getting away from the fact that the character spent a worrying amount of time (especially in seasons 1 to 4) being kidnapped, tied up and drooled over by freaks and fruitcakes. Mulder had a tendency to rush headlong into dangerous situations which usually lead to Scully having to save his ass, so maybe it doesn't count.
Yeah, Mulder seems to get captured/injured/drugged/whatever just as much as Scully does, often because he doesn't stop to actually think before he does something. It was one of the earliest shows to divvy up the proportion of Distressed Damsel and Distressed Dude pretty equally between the male and female protagonists.
Scully did seem to get Bound and Gagged more often than Mulder, Doggett, or any of the other main characters though, so there may still have been some Author Appeal at play.
Mrs. Peel from the original The Avengers series. Almost all of the episodes feature her in some kind of predicament, generally clad in tight fitting (not to say clinging...) apparel and bound in a weird situation. Examples are: tied in aluminium foil to act as an electric conductor to electrocute Steed when he touches her, tied to train tracks (classical but effective), bound to a Mad Scientist patented reclining table to act as guinea pig for his super strong laser, tied, scantily clad in a harem outfit...
The episode where she's locked in a gilded cage wearing a very skimpy feathered costume.
Jeremy Clarkson tried to take advantage of this on Top Gear when he drove his Toyota into a ditch and then called emergency services, claiming to be a pregnant woman about to be eaten by dogs (rather than a fat, old man who can't judge terrain).
This works if you're not Jeremy Clarkson — the AA prioritises "lone woman" calls, as well as some other categories like disabled drivers.
Frequently subverted on NCIS, where Team Gibbs often race to rescue the damsel in question (usually Abby), only to find she's overcome the villain by her own efforts. That's a testimonial to team spirit.
Used not infrequently with Gwen in Merlin. It hasn't started becoming annoying quite yet, but the jury is still out on how many more times a plot can revolve either around her putting herself in a situation (however morally justifiable) that requires Arthur to half-kill himself just to get her out of it (a la The Last Dragonlord), or around her being rescued successfully, only to fall over about seven seconds later and end up needing saving all over again (Lancelot and Guinevere, I'm looking at you.), before things start getting really tiresome. She's the only main character in the show to lack either magic powers, or having been trained to be a Knight In Shining Armour since childhood. And, like Smallville, every character that's not Merlin ends up with the role in at least one episode, including the future King Arthur.
As of Servant of Two Masters and Tears of Uther Pendragon Part One, Merlin has joined the roster. The show is a World of BadassIn Distress.
Elena in The Vampire Diaries, more often than not. Justified as she is the only main character who doesn't have any sort of magic ability. She is constantly being threatened and/or kidnapped to enrage Stefan or sometimes Damon.
Then again, the first time a vampire tried to kidnap her, she didn't just take it and wait for Stefan to save her, she fought back and tried to kill the vampire with a pencil.
Caroline also filled this role, especially in early Season 1, but since she Took a Level in Badass, not so much...
Though Veronica, Sarah, and Sofia all get this at one point or another in Prison Break, LJ is the epitome of this trope. Any time he's on screen he's either being used as a bargaining chip against his dad and uncle or being rescued by his dad and uncle; the kid spends most of the series tied to a chair. All of them though are justified, since they're average citizens stuck in a mass conspiracy against people trained to make them this.
As the one on the show who puts himself in situations he's not equipped for, Rick Castle is usually the one in distress, but in the fifth season episode "Target", his daughter gets kidnapped.
The Hardy Boys Nancy Drew Mysteries: Nancy Drew was reduced to this in second season, once Janet Louise Johnson took over the character, in cross-over episodes with the Hardys. Nancy only existed to be placed in situations that required Frank Hardy to rescue her:
Arson & Old Lace: Nancy gets kidnapped and needs Frank to rescue her.
Voodoo Doll: Nancy wanders into the Big Bad's lair, gets caught, and needs Frank and Joe to rescue her.
Mystery on the Avalanche Express: Nancy gets cornered on a train by two men — a passenger train, in a hallway where there's plenty other passengers in compartments — and can't simply push past them until Frank comes to her rescue.