Gender Equality, Part 2 (Tifa Rule): If any female character, in a burst of anger or enthusiasm, decides to go off and accomplish something on her own without the hero, she will fail miserably and again have to be rescued.
Digimon Adventure: WarGreymon participates in every fight with the Dark Masters. He spends most of each fight firmly clenched between teeth, manipulated by an opponent, paralyzed by hunger or transmogrified into a key-chain. His allies often have to rush to his rescue due to his rushing into fights.
Digimon Adventure 02: Sora Takenouchi got hit upside the head with one of these during the Christmas episodes, by panicking when debris started falling around her and having to be pulled away by Matt; the other characters (including Sora's Bond Creature) ran away. "Chickification!" fans screamed. Sora did recover and joined Miyako/Yolei in the World Tour arc, leading the Russian Digidestined. Unfortunately, that mission didn't go too well either; the girls nearly froze to death and had to be rescued there as well.
Flame of Recca Mikagami Tokiya picked this up, twice, despite his status as "the most cruel" of Hokage and one of the more efficient and intelligent fighters. First, in Sealed Lands arc. After completely ousting Mokuren and Mikoto in a 2-on-1 fight, without chance of recovery, he's pitted against Aoi, who completely overwhelm him stats-wise, even if he has recovered. The result is very obvious, he completely lost it and was later crucifixed and used as a hostage. And then in SODOM arc, he's was forced to pick up another ball for comic relief, where he fails to notice a drugged teacup and then was in turn... strapped into a mechanism, whereas people with less intelligence like Domon slips out of it (in his defense though, his perverted tendencies saved him), and after being pulled out of it, Mikagami was rained with taunts like "So much being the genius!"
It's later shown in the PlayStation 2 game Final Burning that instead of getting suspicious and try to drink with the teacup, Mikagami can opt to say "Sorry, I'm not thirsty" and just avoid all those embarrassment. But apparently, in the manga, he was holding the Distress Ball, so obviously (and gratingly), he did not pick that option.
Faye in Cowboy Bebop's Episode 5 tries to find out who murdered Mao Yenrai on her own, but winds up captured by his murderer, Vicious, and his Red Dragon goons. Spike heads to the church to take Vicious on, but does take the time to save Faye when a Red Dragon mook tries a Put Down Your Gun and Step Away.
Carrot Glace in Sorcerer Hunters is shown to be more than capable in a fight, but several times he's become a Distressed Dude and needed the rest of the team to bail him out. Though to be fair, this usually happens due to his Idiot Hero status.
Akane Tendo in Ranma ½. The girl was first shown beating up fifty-odd armed attackers on a daily basis and was called Champion of her Martial-Arts School. Yet on more than one occasion, she gets kidnapped by opponents, far, farbeyond her level, and acts like a complete ingenue (one kidnapper tied her up with pantyhose for pete's sake!) Of course, once the immediate threat is absent, she does her damnedest to try to escape.
Mokuba gets kidnapped roughly once-an-arc, and briefly possessed in an Anime-only arc. Granted, unlike most of the examples, he's just a pre-teen with some improbable skills. One wonders why Seto Kaiba doesn't hire some competent body guards, or better yet chain his brother to him by now!
In the original Yu-Gi-Oh! manga, Anzu attempts to lure Dark Yugi into the open by riding a Ferris Wheel with bombs underneath each of the cars. Too Dumb to Live, indeed.
Asuna also falls into this sometimes, although it's less of "picking up the distress ball" and more "got hit on the head with the distress ball".
During the Wilhelm arc, about a third of the class gets hit with the ball.
Butt Monkey Matsuda from Death Note picks it up, but he handles it with almost uncharacteristic competence after he's in over his head.
Jinpei in episode 8 of Science Ninja Team Gatchaman. Bothered by his alter ego The Swallow's lack of popularity, he decides to go off on his own to save their new underwater base from Galactor and to show everyone just how heroic The Swallow really is. Naturally, he gets nabbed by Katse and has to call the rest of the team for help.
World Destruction: Kyrie from the anime picks this up every other episode. Despite the fact that he is a capable fighter in the game and he has the power to destroy the world, Kyrie never arms himself with anything and must rely on his friends Morte and Toppi to bail him out. He manages to subvert this slightly in the manga as the only reason he picked it up was because he froze in place. And despite the fact that he can fight in the video game, he still gets himself captured.
Fairy Tail: Erza Scarlet, usually the most competent of the main cast, is quite happy to paint a target over herself whenever Jellal in any way becomes involved with the current action.
Asuna Yuuki from Sword Art Online during the Fairy Dance arc (episodes 15-25 in the anime, volumes 3 and 4 in the Light Novel). Although her dis-empowerment is more or less justified in-universe and at least tries to escape on her own (and manages to go pretty far), there are moments where her Action Girl attitude is completely gone.
Buffy Summers form "Buffy The Vampire Slayer" season 9 comic. She is supposed to be this great vampire Slayer, yet almost every time we see her she is defeated, humiliated, kidnapped, betrayed, she always need rescue and she can't do anything right. First she got drugged and her body is stolen from her. Then (issue 2) she lost fight with single zompire and she must be rescued by Severin. Then (issue 4) she was lured into a trap by Severin and must be rescued by detective Dowling. Then (issue 7) she got her arm torn off by a single zompire. Then (issue 9) she is kidnapped and in issue 10 Spike, Andrew and Spike's cockroaches must save her. Then (issue 11) she fails to stop assassination attempt - fortunately this was just a drill. Then (issue 12) she is almost smothered to death by tentacle monster and must be rescued by Kennedy. Then (issue 13) she is defeated by Eldre Koh who cut her face. In issue 16 she got owned three times in a row by single zompire. And in issue 18 she will fight Severin, a guy who almost killed her before. Severin is a human who draws powers from supernatural beings but can be hurt with a gun, and instead of using a gun on him, Buffy go against him with her superpowers.
Given to all of Equestria in My Little Unicorn, when Nightmare Moon and her allies enslave the place without much resistance and take Luna and Celestia hostage. Naturally the Unicornicopians have to come for the rescue.
Inspector Chan from Sha Po Lang, after losing three of his four men to the rather psycho assassin played by Wu Jing and his badass kung fu, decides to go after the guy's boss, Wong Po, all by his lonesome. He storms the guy's HQ and does a fair job of blowing away Wong's mooks, but when he finally confronts Wong, being as this is a kung fu movie and not a gun fu movie, he promptly gets owned by Wu Jing and captured by Wong, which means that Donnie Yen has to save his ass in the final showdown.
Happens in Septimus Heap, where Sarah Heap in Darke runs back into the Palace after her duck and is overrun by the Darke Domaine mostly so that Simon can rescue her later.
Laurana from Dragonlance gets passed this in Dragons of Spring Dawning, when, after having been previously shown to be a brilliant military leader, she suddenly accepts without question a message from her Arch-Enemy, Kitiara Uth Matar, claiming that their mutual love, Tanis Half-Elven, is with Kitiara but has been mortally wounded and wants to see Laurana before he dies. Laurana believes the message even though Kitiara: has an obvious motive to want to harm Laurana; provides no proof Tanis is even with her much less that he is dying; and requires Laurana to come to the meeting site without any guards. Laurana's friends Flint Fireforge and Tasslehoff Burrfoot even try to warn her that the message is obviously Schmuck Bait, but Laurana is absolutely certain she can trust Kitiara, so she goes to the meeting site without taking any precautions and is promptly betrayed and captured and ends up having to be rescued by Tanis.
In fairness Laurana, while far stronger and smarter than the Brainless Beauty she seemed to be during her first appearance, is still someone who just hasn't had that much experience of the wider world (even in Dragons of Spring Dawning she's only been away from elven society for a year or so). She hasn't completely lost her naïvity and faced with the possibility that Tanis is dying she isn't thinking too clearly. It was stupid yes, but a moment of in-character stupidity.
In the Annotated Dragonlance edition, the authors acknowledge that Laurana's character development at this point meant that it was stupid and out of character for her to do this. But they had to do it for the plot's sake, making it a perfect example of this trope.
Dawn from Buffy the Vampire Slayer falls prey to this a lot. Hey let's go out with people I don't know, at night, in Sunnydale. That's not suicidal.
The Doctor's companions in Doctor Who tend to carry these around a lot. The Doctor himself points it out in the episode "The Empty Child", muttering about how he always tell them not to wander off alone and how they never listen.
Lampshaded often, including in The Two Doctors:
Second Doctor: Now Jamie, stay with me, don't wander off.
Gender inverted in Farscape a couple of times, generally involving John storming off the ship in his module for one reason or another and getting stranded. Parodied and lampshaded in the episode "John Quixote" when John finds Aeryn dressed as a princess on the top of a castle asking for help John then says "Now I know somebody is messing with us".
There tend to be a number of them every episode of Ghost Whisperer. Although there are plenty of subversions too — Melinda will often do something very stupid and dangerous, but nothing will come of it.
"Arson & Old Lace" has Nancy held captive for six months. By an old man in his 70s. In a penthouse. With a phone and an intercom to a secretary who's not in on the plot. With an elevator that doesn't require any special code to operate, that leads right down to a very public and open office area. No, she's not tied up. She's not held under lock and key. And somehow the elderly gent is able to force her into an elaborate dress and hairstyle, too. She just passively waits for Frank Hardy to rescue her as the building is burning down.
"Voodoo Doll". Nancy goes off on her own to investigate the Big Bad. Yup, gets caught. Yup, is held captive (again, untied up) with two other women, similarly untied, in an open warehouse with tons of crates. The only door INTO the warehouse area is locked. On Nancy's side of the door. With the hinges on HER side, too. Her one attempt to escape involves her climbing UP crates to go through a window, and is promptly caught. It takes the Hardys breaking into the warehouse through said door before Nancy can escape. *sigh*
Kate from Robin Hood. Technically she is a full-time Damsel Scrappy, so perhaps doesn't fully belong here, and yet the writers' dependence on using her to kick-start plots by having her acting stupid (to the point where the character served no other purpose) and the fact that she never manages to extract herself from any of the danger she wanders into means she deserves a mention.
In her first episode she abandons the outlaws in order to try and rescue her brother on her own. Naturally, she's captured in under five seconds and her brother is killed as he tries to rescue her. Two episodes later, a tax collector begins swaggering around Locksley; Kate decides that the best way to handle the situation is by loudly bad-mouthing him in front of everyone. He captures her and the outlaws have to drop everything to go and save her...twice. In the sixth episode she doesn't get out of the way of a dagger being thrown at her, and spends the rest of the episode being tended to by the other outlaws (this includes her getting spoon-fed). One episode later she's captured yet again (off-screen) because apparently she couldn't run away from the guards fast enough, and in the episode after this she is captured by a soldier (by not being stealthy enough) and is then almost raped in a bar tavern. In the second-to-last episode she storms into a peaceful sit-in protest, ranting and raving and hurling abuse at the soldiers for no apparent reason, and is about to be killed when another outlaw intervenes, effectively beginning a fight. In the grand finale, she's - you guessed it - captured yet again, offscreen again, and the outlaws have to save her again (although in context this capture was more justified than the others).
The members of Torchwood just can't seem to stop meddling around with mysterious alien artefacts whenever the plot needs to be kicked off.
That actually makes perfect sense. Shadows do not attack normal people, as they do not perceive them as a threat. They only attack people with Personas, unless the Shadow in question belongs to the person currently in the TV world.
Princess Peach has handled this ball a few times in her career. A few others, things are just out of her control. A few other times, she's seduced by cake.
And even Mario is not safe. He wandered off into a haunted mansion by himself in Luigi's Mansion. The result is... predictable.
Happened again in Luigi's Mansion: Dark Moon, where he somehow just captured by King Boo just before the story started. It's never really explained why Mario got captured, but it's possibly because he was the first guy sent in to deal with the problem by E Gadd and it all went wrong from there.
Slightly averted in Super Princess Peach; one of Bowser's Goombas slipped in with the Vibe Scepter and zapped everyone - itself included - into emotional insanity, plumbers included. Peach, Toadsworth, and another escort happened to be Late to the Tragedy.
Everyone picks up one in Mario Party DS. Oh Hey! My Archenemy just invited us all to dinner! He's tried to take over the world, kidnap us, and kill us all in the past... But hey, free food!
Mario Is Missing. How can he not have anticipated the consequences of always using the front door?
In Metroid: Other M, when Samus encounters Ridley, she becomes terrified and is unable to fight back. Ridley easily grabs her, leaving one of her allies to begin the offensive in her stead. There are arguments over whether or not she had the distress ball at the time, since she had traumatic childhood memories regarding Ridley, but has also faced and defeated him numerous times in the past without an emotional breakdown.
Bastila:"Rescue me? Is that what you thought you were doing?"
In Fire Emblem 8, if you choose Ephraim's route, Princess Tana of Frelia (a Pegasus Knight who has just finished her training) will try to follow him to war against orders of her father and brother, only to get herself captured; therefore, one of your purposes in the following stage is to rescue Tana and give her the weapons she needs to join the group. Note that in Eirika's path, Tana offers her help directly to Eirika from the very beginning, so the hostage situation doesn't happen and you can have her in the party from the start.
This may have come from Fire Emblem 6, where Magical Girl Lilina is trapped in her own castle by her enemies and locked in a room. Just like in Tana's case, as soon as Roy rescues her Lilina joins the party.
On the other hand, early before the route split, Ephraim and his knights, Kyle and Forde, suddenly needs to be rescued after being betrayed by Orson... or so it seems when suddenly the trap turns into Eirika and company, now they need to be rescued... by Ephraim and company.
Kazooie picks up the Distress Ball in the early stages of Banjo-Kazooie: Grunty's Revenge, where she's kidnapped by Gruntilda. Sort of. It's actually the result of time travel. Mostly... Point being, you have to rescue her (and a bunch of other trapped Breegulls) from the second level before you can use her powers. Even the manual says "She just wants to get back to her best friend and back to kicking Grunty's butt."
Adelle briefly leaves the clan in Final Fantasy Tactics A2. Guess what happens? The Big Bad, who expressed interest in her abilities as a Gifted before, brainwashes her, of course.
Rinoa Heartilly of Final Fantasy VIII loves her Distress Ball. She probably even named it. She foolishly goes after the Sorceress intending to bind her powers with a magic ring (a plan which admittedly could have worked had Quistis not ignored it) but ends up in a trance and attacked by Iguions. Naturally she must be saved. She ends up falling off the side of the Garden and hanging on waiting to be rescued, ultimately ending up in a coma at the end of Disc 2. The end of Disc 3 is her inexplicably wandering off and getting kidnapped by Seifer. This is balanced out somewhat by moments of competency such as leading an attack on the prison to rescue the others and gaining Sorceress powers to become a Game Breaker.
Planescape: Torment: The mastermind behind Morte's 'skullnapping' in was a being of such immense power that he could permanently kill the Nameless One, but still, with a pair of wererats? At this point in the game, Morte could solo rooms full of them.
Right at the beginning of Beyond The Beyond, Annie takes the Distress Ball and runs into a cave with it, after her father, a seasoned knight, refuses to let her go out adventuring. She promptly gets trapped and nearly eaten by a cave beast, and it becomes the duty of Finn, the hero, to go to the cave and save her.
Yggdra in Yggdra Union fits this trope perfectly when she goes off after Gulcasa.
World of Warcraft: Jaina and Sylvanas both try in vain to confront Arthas directly in the Halls of Reflection dungeon. Jaina probably fits more, trying to appeal to his last bit of humanity instead of revenge, but they both fail and have to be saved by the players... who then in turn are saved by their faction's airship.
In Breath of Fire, shortly after Ryu arrives at Winlan, the player gains control of Princess Nina as she decides to storm the lair of a powerful wizard to obtain a cure for her poisoned father (who the wizard was responsible for poisoning). Granted, she does (or rather, is forced to) take a pair of soldiers with her as bodyguards, but all the same, she is captured and needs to be rescued by Ryu afterwards.
In Star Ocean: The Second Story Rena carries this for the very early part of the game, as the girl with mysterious magical powers and (according to her character profile) martial arts training ends up being kidnapped, going along with her kidnapper (to save her mother,) then trying to escape and bumbling right where her assailant wants her to be - all so that Claude can show up and save her. Fortunately, she mostly gets to drop that ball after the rescue is finished.
There's an interesting case in Odin Sphere. Oswald, the unstoppable Shadow Knight, proves unexpectedly unequal to the task of fighting the baby dragon Leventhan when Fire King Onyx sends him to do - in spite of the fact that Oswald has by that point already killed two fully-grown adult dragons. Coming fresh from fighting Onyx himself to a standstill may have something to do with it. Fortunately for Oswald, his wife Gwendolyn is willing and more than able to swoop to his rescue, smack down Leventhan herself, and royally bitch Onyx out for trying to Murder the Hypotenuse.
The entire f***ing plot of Nine Hours, Nine Persons, Nine Doors was set into motion because Akane went back to retrieve the doll that Junpei had given her, which she'd dropped exiting the vent that Seven had led the children out of, thereby getting herself thrown into the incinerator room alone during the first Nonary Game. Compare this to the hypercompetent strategist Zero, architect of the second Nonary Game. It's the same girl. The mastermind behind the plot was setting up a Stable Time Loop to save herself from her own stupidity.
Starfire in Teen Titans: Trouble in Tokyo. She actually forgets that she can fly and has to be snatched out of the air mid-drop by Robin, who has no super-powers. Ironically, one fan once remarked on a forum that if such a thing ever happened she would be called out on it, as it would be an obvious ploy to attract Robin's attention. Instead it was played painfully straight.
Well her powers are emotion based and it wouldn't be the first time she lost them due to issues relating to Robin...
In Transformers Animated, episode 2, Prowl, The Lancer of the team, tells Optimus Prime that there's only one person he trusts. Himself. He promptly gets sucked into a nanite monster and almost killed were it not for his teammates. In fact, despite him being the best fighter of the team, Prowl catches the Distress Ball quite a few times in the series, usually after trying to do something alone. Maybe it's trying to send him a message?
Daphne from Scooby-Doo. The girl's entire purpose was to be "Danger-Prone Daphne", as they called her. (Note that this chiefly references Daphne from the cartoon series. In The Movie, she's more action geared.)
Code Lyoko: Aelita has a tendency to pick the Distress Ball in Season 1 and 2 by not always waiting for the Lyoko Warriors' help. Worst case is certainly in episode "Uncharted Territory", where her difficulties to adapt to life on Earth spurred her to return alone on Lyoko, right into XANA's trap. Almost as bad is episode "Déjà Vu", but then it was XANA's entire plan to tempt Aelita into going by herself in Sector 5.
Contrary to popular belief, this concern Yumi much less despite her Designated Victim status. When she puts herself in danger, she knows what she's doing and has a damn good reason for it (like in episode "Hot Shower", to save her little brother).
Kim Possible. 90% of the times when either hero (yes, both Kim and Ron) decides to do a mission of their own, they will be captured.
Iron Man: Armored Adventures has Pepper Potts hold this most of the time. Occasionally she'll pass it to Rhodey and be competent for an episode, but the next episode we're right back to her being too dense to do anything but sit dumbly in the middle of a room where two factions of the Chinese mafia are duking it out.
The Wasp, the only female Avenger during the first season of The Avengers: Earth's Mightiest Heroes, gets captured at least three times during the first 27 episodes, and becomes unconscious in four episodes, including one instance which occurred after she became the first Avenger to succumb to a burst of gamma energy.
One time, she got captured, and three of the male Avengers became kidnapped after her.
Pearl friggin' Pureheart from the original Mighty Mouse cartoons. In the Bakshi retool, she's usually quite capable of handling things but still requires the hero's assistance in dire situations once in awhile.