Princess Lurichiyo. A bratty, spoiled rich kid who can't seem to stop getting kidnapped. After Ichigo and crew have the kidnapper cornered and it looks like the filler arc is over, Amagai shows up, reveals he is a villain, and kidnaps her again. Made more irritating for some by the fact that the arc came up in the middle of the Hueco Mundo arc and after Ichigo's battle with Grimmjow.
During the Arrancar arc, Orihime also got this reputation among parts of the fandom.
Beauty from Bobobo-bo Bo-bobo serves two purposes: perpetually reminding the viewer at the top of her lungs that the things the other characters are doing are bizarre, and being the Distressed Damsel when the plot calls for it.
Miaka from Fushigi Yuugi, despite being the series protagonist, has come in for some fan hate for the numerous times she pointlessly rushes headfirst into dangerous situations, in some cases even actively sabotaging her protectors or not telling them important information, then getting in trouble and needing them to come save her anyway.
One of the reasons why Akane Tendo from Ranma ½ is considered by some to be a Base Breaker is the fact that, sometimes, she comes off as one of these. It's not that she gets kidnapped a lot (in fact, Ranma Saotome himself is actually kidnapped more frequently than she is), but she does get into trouble frequently, often because of her own issues (temper tantrums, pride and blind distrust of Ranma/trust of her enemies, mainly), and usually ends up contributing nothing positive to the experience. The very earliest examples of this are the Martial Arts Rhythmic Gymnastics and Martial Arts Figure Skating stories.
Molly from the English dub of Sailor Moon. Her horrible accent, combined with how she gets attacked by the Monster of the Week in almost every episode of the first season, makes her much more annoying than her the original character.
Chibiusa/Rinni too. Over half of the Monster of the Week plots in the second season are kicked off by her running off and getting herself into trouble. You'd think the girl would cop on after it happens so many times but no. The villains of that season have the easiest job in the world - they don't have to try and find her at all, they just need to wait for her to run off and inevitably reveal herself which happens every time.
Mokuba Kaiba from Yu-Gi-Oh!, who gets into trouble precisely seven times in the series. However, he's not all that hated by fans since he's a kid, which makes it a bit more understandable as to why why fully grown people are often managing to kidnap him, and often more amusement than annoyance is found at the fact that he's in trouble so often. And to his credit, in one memorable situation, he actually manages to break himself out, finds Yugi and Kaiba with a helicopter, and takes them to where Yugi's friends were being held captive.
This is the characteristic once strongly associated with Lois Lane. Ironically, it can be argued that Lois' role as a Distressed Damsel was far more important to the Superman plot than her role as a love interest, Depending on the Writer. In the 1940's, she did need to be rescued a lot (usually while pursuing a news story), but was fairly intelligent and could sometimes get herself out of scrapes by kicking ass and taking names. Once the 50's, 60's and early 70's came around though... Yeesh. She was an empty headed twerp who was constantly putting herself in danger for no reason, and whose sole goal in life was to trick Superman into marrying her. She took Too Dumb to Live to uncharted levels. In recent comics and other media she's a much more well rounded and developed character, who is extremely competent and able to take care of herself. She still needs to be rescued sometimes, and the trope may pop up occasionally, but for the most part she's a very independent, intrepid and intelligent reporter who just needs a little help against super powered aggressors from time to time.
The sixties-era book Superman's Girl Friend, Lois Lane seemed dedicated to making sure every single reader hated poor Lois. If you Google around, you'll find scans of multiple letters columns where readers asked for Superman to spank Lois (which would in fact occur, though in the context of Super Dickery). A few may have had other motives than scrappyhood, though.
Even when there's neither any Super Villain's ill will nor a big scoop one jump away from her window, she can be trusted to find something dangerous. Letters on the label are bigger than her eyes, so... they just don't fit in, right?
Starting late in The Seventies comics, Lois was written to be more assertive to avert this trope, and needed rescuing much less often, including in her solo stories in The Superman Family. This included Lois having mastered a Kryptonian form of martial arts named "klurkor."
Being associated with this trope is probably what spurred John Byrne, in his Post Crisis retelling of Superman's origin, to make it very, very obvious that Lois was now a Badass Damsel bordering on Action Girl. This eventually led to an Inversion immediately after her wedding to Clark when he was kidnapped after temporarily losing his powers. Lois took her Army brat background to extremes, becoming a G. I. Jane in order to come to the rescue.
Parker from Frozen. Audiences blamed her for getting herself, her boyfriend and his best friend all stuck on a skilift during a snowstorm, she survives the ordeal and has the massive luck of finding a road where she could be rescued.
Mary Jane Watson from the film franchise. Three movies. Three times kidnapped to be used as bait to lure Spidey out. Yawn. Spidey rescued her three times in the first movie alone. A real shame considering one of her signature comic book traits.
Lampshaded in the third movie novelization by Mary Jane who asks if she has bait stamped across her forehead when she's locked in Venom's falling car. Also in the third movie, MJ does become a Heroic Bystander and drops a block of cement on Venom's head as he fights with Spider-Man, and to her credit, she tries to attack Doc Ock from behind in the second film, but Aunt May had already successfully done the same thing earlier on, and Doc Ock doesn't repeat his mistakes.
Interestingly enough, Gwen Stacy was originally going to be the one abducted for the final battle in the third film, not Mary Jane, and Mary Jane would have been the one who helped Harry come to his senses. A line from this was included in the trailer: "We've all done terrible things to each other, but we have to learn to forgive each other or else everything we ever were will have meant nothing."
If you listen to the DVD commentary, you can hear the irritation in Sam Raimi's voice while he recalls having to A) put MJ back in the damsel role because of time constraints and B) having to apologize profusely to Kirsten Dunst after he promised her before the filming of the movie that she wouldn't be doing that again.
Bella Swan pretty much epitomizes this trope, even commenting in her own narrative that "I guess my brain will never work right. At least I'm pretty." Add in the fact that she can't seem to get out of any scrape without the intervention of a male, you've got one of the most textbook examples of this trope EVER.
Clio Marsden starts out like this in E.E. "Doc" Smith's Triplanetary (the first of the Lensmannovels), but gets a lot better as the book goes on. In her case, the threats ("a research upon sex") are anything but vague.
The entire Tribe Of Rushing Water in Warrior Cats. In only one of their four appearances did they not need to be saved from something by the clans, yet they are rude to the clans and tell them to go away. In Sign of the Moon, the cats come for a visit when the Tribe doesn't think they need help and the Tribe actually attacks them!
Millie in Castle Roogna. She repeatedly gets kidnapped or attacked, and never does anything to defend herself other than by kicking (not kicking the assailant, mind you, just kicking in the air) and screaming.
Nora Grey, the heroine of Hush, Hush, quite possibly gives Bella a run for the money. Over the course of three books, she repeatedly walks into dangerous situations without telling anyone else where she's going (so no hope of a rescue if a plan goes wrong), no weapons of any kind, and usually no actual planned course of action beyond "I'll break into that place and wing it". The author seemed to be trying to channel Nancy Drew, but failed to give Nora any competency. Really, Nora's stupidity could be summed up near the end of the first book when she willingly walks into an empty school and plays into the bad guy's hands, even though (A) she knows she's being lured into a trap, (B) her super-powered, invincible boyfriend is already rescuing the hostage being used as bait for Nora, and (C) the bad guy doesn't even know said boyfriend is on the case, meaning that if Nora had stayed put, the entire climax probably would never have happened. And then, when she's in the school, she gives up and says that she hopes her boyfriend will rescue her. Even though he has no idea she is inside because he told her to wait outside for him.
Kimberly Bauer, former Trope Namer, has an annoying habit of getting Trapped By Mountain Lions, wandering around bra-less in wifebeaters around potential rapists, and doing everything in her power to anger men with guns. Kim is sometimes known as "Bathroom-Break Bauer", due to a nearly-unbroken string of kidnappings, confinements and hostage-takings, which make it possible to take a bathroom break whenever she's on screen without missing anything truly important. The writers have admitted, in essence, that she can't be killed off because Jack has already lost Teri, his wife and it would destroy him.
Tegan—though, as a woman of normal intelligence stuck on the TARDIS with three alien super-geniuses (The Doctor, Nyssa, and Adric/Turlough), she was Damsel Scrappy By Default. You want real a Damsel Scrappy in Doctor Who, try Vicki, Victoria Waterfield or Peri Brown.
Mel was the only companion during her tenure, and thus had the duty of getting captured. This would be fine if she were useful or likable. And then she was followed by Ace. Who killed Daleks with homemade explosives (stored in deodorant cans) and a super-charged baseball bat.
Matlock: Charlene Matlock, who almost every episode gets herself into some sort of trouble by trying to investigate/snoop around alone and either Ben or Tyler need to come to her rescue.
Revenge: Charlotte. People were not fond of her by the end of the series, but she arguably got the most blow back from every revelation Emily reveals.
Revolution: Charlie. What were the creators thinking making her the main protagonist? Taken Up to Eleven in "Soul Train." There is something seriously wrong if Danny has to save your ass from getting choked to death. Then again, she hasn't received proper combat training, and she was taking on The Dragon and Scary Black Man Captain Tom Neville, so she needed help! Fortunately, they've started redeeming her; Spiridakos seems to be a little less wooden now, and the character is really becoming effective with her weapons.
Robin Hood: For this BBC show, a number of viewers feel that the replacement for Marian, Kate, fits this. She's pushy, loud and generally useless, where in contrast the previous character in the love interest role was an Action Girl who at least had the dignity to be right when she was pushy, and was never louder than was needed. And yes, true to the trope, all of Kate's numerous kidnappings were due to her inability to keep up, defend herself, or know when to keep her mouth shut.
In her capacity as a "damsel" scrappy, she's been captured by guards more times in one season than any of the other outlaws have in three. The words: "Where's Kate?" could be a drinking game.
Jennifer Keller', though she learned to fight in the final season and part of the Scrappy-ness has to be from her replacing Carson Beckett.
Fans are probably also willing to cut her more slack because her actress is associated with a well-liked former role. Or that may paradoxically lead some to dislike Keller because she's not Kaylee. Ah, human nature, you never fail to amuse with your delightful contradictions!
Stargate Universe: Chloe, who was - like Jennifer Keller on Atlantis - the Love Interest for two different guys. Unlike Keller, however, Chloe had virtually no useful purpose whatsoever.
Olive Oyl from Popeye. Much more so in the cartoons, especially the Famous/Paramount Studios ones.
One of the most annoying was Sharmell Sullivan, 1991 Miss Black America and the wife (both on-screen and off) of former WCW great Booker T. Beginning in 2005, Sharmell accompanied Booker to all his matches dressed "beauty queen" style in a fashionable gown and tiara, and sometimes petticoats as well. Her only purpose when she and Booker were faces seemed to be getting menaced by her husband's heel opponents (including Kurt Angle, who notoriously threatened to rape her). While Sharmell was capable of giving some of the weaker villains a good slap across the face from time to time, for the most part she was reduced to shrieking "BOOK-ERRR!" until her husband could come in to save her. After the pair's Face Heel Turn (and especially after Booker became "King Booker"), Sharmell became more of a Faux Action Girl (with a bit of the Alpha Bitch thrown in). At the 2006 WrestleMania she even joined Booker in a handicap match against The Boogeyman - but the pair lost when Boogey grabbed Sharmell and shoved a handful of worms down her throat!
Vickie Guerrero as well, with a side order of Miles Gloriosus to boot. As General Manager of Friday Night SmackDown, Vickie would boss around all the fan favorites in her obnoxiously whiny voice and generally act like a bitch....until someone like The Undertaker would threaten her, and Vickie would turn into a cowardly Screaming Woman who was helpless until her love interest of the moment could come rushing to her rescue. She eventually did Take A Level In Badass and even wrestles occasionally, but at heart her character is still a man-hungry Mrs. RobinsonWannabe who pouts when she doesn't get her way and still screams all the time (particularly when her newest boyfriend, Dolph Ziggler, is losing a match).
If one does the math, Peach has been kidnapped a grand total of 21 times (counting twice in Super Mario 3D Land), and only five times was the culprit not Bowser (which may make him a Damsel Scrappycreating Scrappy for some.)
Rinoa from Final Fantasy VIII gets blamed for this, managing to get herself kidnapped four times through the course of the game, but only on the first instance did her own foolishness get her into the situation. The rest was unfortunate circumstance. The thing that grates most players is how accepting the rest of the cast becomes afterward—at one point, even choosing to save Rinoa despite the fact that saving her conflicts with Squall's (the player's) current task as leader. They get mad at you for even considering that the mission may be more important than saving her. It also doesn't help her out that the other two playable females, Quistis and Selphie, are highly-trained military professionals, while Rinoa is an untrained teenage girl (though ironically....)
Also, Rosa from Final Fantasy IV, who spends the whole first half of the game in distress, gets this reception from some, even though she makes up for it in the game's second half as the White Magician Girl.
Rosa potentially gets worse by the sequel, the After Years as she now only exists as a Damsel In Distress to give character developments to "Ceodore! Cecil! Kain!" and spends one climax getting dragged around forcefully by Dark Kain.
Princess Elise from Sonic The Hedgehog 2006. Throughout the course of the game, she gets kidnapped by Dr. Eggman three times.
The Damsels in Spelunky are pretty much based on Willie Scott and manage to work this trope into game mechanics. Though they aren't *that* annoying, some players still delight in throwing her at spiders, attaching a sticky bomb to her and sending her charging towards enemies, and then throwing her corpse at more spiders.
Shirley Fennes from Tales Of Legendia, along with being the game's plain Scrappy. Though to be fair, in the Character Quests following the main scenario, she became a party member and only got kidnapped once, by Jay, whom she actually ended up helping during this situation through being a Badass Damsel.
Colette Brunel from Tales Of Symphonia. Despite that she does get better after a little while (and that technically, Mithos can kidnap ANYONE at the end, even Regal), some people dislike her for this.
Shana in Legend of Dragoon, however, most people preferred her over Miranda, who never got kidnapped or sick but still turned out to be more annoying.
Slippy Toad. Dear lord. A player could be haunted for YEARS with the ear-piercing refrains of "Fox! Help me!!" or "Fox! Get this guy off me!!" If it weren't for his unbelievable mechanical ability, the Star Fox team would have probably pushed him out an airlock after his first mission.
Ninian from Fire Emblem: The Blazing Sword often gets lumped into this category, even though she's only ever captured twice and the third time she goes with the Big Bad willingly to spare her friends' lives.
Leon could also be blamed for being a Failure Hero since he is always besides Ashley but can't do anything to save her. Granted, he can't fly after her the second time and can't control the parasite in his body the third time, but the blame for Ashley's first capture is all hers because she stupidly pushed him away and tried to run off.
Yukimura Chizuru from Hakuouki comes in for a lot of frustration from players for her lack of combat ability and reluctance to fight, which - since she spends all her time in the company of the Shinsengumi and is herself the target of kidnapping attempts by demons - makes her The Load and means she repeatedly has to be rescued by others.
Denny Levens serves three basic purposes in Candi's life: provide her with a new last name, give her someone to constantly protect/rescue, and give her more issues to Wangst about when her effort to do so fails in the long run. Given he used to be a bootlegger, and he's now in a war where his enemies want his wife's head for a trophy, it'd make sense that he'd learn to wear a bulletproof vest or stock up on an assault rifle. Nope. He buys a wimpy pistol, that jams. And he immediately ends up being beaten half to death with a bookcase.
As a bonus, he considers Scrappy as a Damsel Scrappy in this list, seeing as he's really always outmatched and in danger but is too hard-headed to ever realize it. Shaggy and Scooby usually always have to pull him away before he gets himself hurt or killed.
I'm starting to think that Bucky must have a tracer planted on him that allows Captain America to track down these hidden enclaves of enemy combatants. That's the only possible use I can think of for a sidekick who's only contribution to the war is to get captured every month...
In-universe examples: Patrick and Esmeralda from The War Comms, always calling for Gordon and Tuxedo Wank Man to save them at the slightest hiccup. Gordon even lampshades this in a comment to Pat during Nancy's intro post.
Norman Price in Fireman Sam. Even on the rare occasions that someone else needs rescuing, he's usually the cause of the trouble.
She is known to often fall into traps, be kidnapped by the villain, or anger the villain in some way. Her nickname in the original Scooby-Doo, Where Are You? series was "Danger-prone Daphne".
The first live action film played with the concept and had Daphne pick up martial arts skillsand become generally more useful after the gang broke up as a direct result of being called out for being the Distressed Damsel. In virtually all Scooby Doo series and films since then, Daphne has been portrayed as a MacGyver with her makeup kit and accessories. Her martial-arts skills from the live action film carry over to the animated film Scooby-Doo and the Samurai Sword, where she arguably has a Crowning Moment of Awesome when she fights in the arena.
In an interview, the staff of that movie said that changing Daphne was necessary for the sake of proper method acting. The goal established from the start was for live actors to do the best interpretations they could of the cartoon characters, but they ran into a roadblock with Daphne because in the cartoon she essentially had no personality. The natural choice was for Sarah Michelle Gellar to channel her greatest known role.
Daphne became more competent well before the live action movie. In the 1980s Scooby Doo series when the group was reduced to just her, Shaggy, Scooby and Scrappy, she became the leader of the group. That also was true in the 13 Ghosts Of Scooby Doo series, where she was the Team Mom. Unfortunately, she quickly lost accumulated good will with the horrendous character design and jumpsuit she had in that series.
The other girl's name is Frieda. Her role in the cartoon was downplayed after giving Virgil a guy best friend instead of letting her be the best friend. She was replaced by Richie Foley, who is basically her except male and blonde - according to Word Of God, he's also gay. On the other hand, Richie also falls into this category in the sense that he's always getting kidnapped and his help is mostly ineffectual except for a few episodes. His ineffectualness begins in episode 1 when he tries to protect Frieda from Hotstreak and gets his shirt burned to a cinder, and he is first kidnapped in the episode "Sons of the Fathers" by Ebon. After that, he becomes a mind-slave twice and is kidnapped at least three more times. However, since he's a male, people love him, even if they're outside of the age group that he was created to appeal to. So he's more of a Damsel Bumblebee than Damsel Scrappy. That, and the fact that Richie gets super powers of his own later on, so he's actually able to help out more in combat and rescues Virgil a few times.
Pepper Potts in Iron Man: Armored Adventures has two purposes for her existence: help Tony out on occasion and get captured and rescued constantly even in situations she should be able to escape from on her own. Her behavior is consistently damsel-like despite her aspirations to be a kick-ass SHIELD agent - at one point she's in the middle of an abandoned warehouse where two different factions of Chinese assassins are fighting and she sits there waiting to be rescued instead of getting away from the fighting. Yeah, real SHIELD material.
Sentinel Prime is an unusual male (not to mention giant alien robot) example. Most of his time onscreen involves him getting into some scrape or another and having the long-suffering Optimus get him out. It seems the only thing that keeps Optimus from abandoning him is a sense of guilt about their shared past and perhaps some level of fondness for his old Academy-mate.
Mix of all of the above, and the hope that Sentinel gets it through his thick head that his arrogance is a Bad Thing. But Status Quo Is God and he always rubber bands back to being a jackass by his next appearance. Even Jazz, who has long tolerated (or ignored) it as his second in command, finally gives up and more or less defects to Prime's crew.
Aquaman, on the Super Friends, sometimes falls into this role. He seems to exist only as someone to get captured by the Legion of Doom, so that the rest of the Justice League can rescue him.
Miko of Transformers Prime. No matter how many times she is told by her friends not to sneak off to see the titular robots fight and get caught in the crossfire, she sneaks off anyway, has to get rescued, and in some cases nearly kills her friends. After doing so, she can be counted on to laugh about how awesome it all was even as the Autobots are trying to make her understand that nearly getting people killed or causing important missions to fail is in fact not a good thing. Being merely Too Dumb to Live would be bad enough, but knowing and not caring because your amusement is more important... she makes people say "I guess Daniel Witwicky wasn't all bad..." Also, she's another one the creators love far more than the viewers, so we get a lot of screentime devoted to someone whose "wacky antics" fall squarely into Dude, Not Funny!.
Greatly improved in season two. She's gone from underfoot and proud of it to actually helpful, caring when people almost get killed, and not being the most common cause of people almost getting killed. All while not becoming unrecognizable. The arc with Bulkhead's injury and recovery have been especially good for her, and prove that anyone can be Rescued from the Scrappy Heap.
Max Gibson in Batman Beyond is often considered this by her detractors. This tendency is best displayed in the episode "Final Cut", where she ignores Terry's instructions and snoops around for clues, leading to her getting attacked by an assassin. Terry has to leave his post protecting the assassin's target to rescue her, which results in the target getting mindwiped with a hidden bomb ready to explode thanks to his Dead Man Switch.
Zoey in Total Drama Revenge of the Island. In almost every episode prior to the merge, she manages to get herself in a hairy situation with Mike coming to her rescue almost every time.