Comic book heroes seem to spend about half their time rescuing some girl they've been dating on-and-off for about seventy years from something each issue, from Olive Oyl to Lois Lane. (Unsurprisingly, people who Love someones alter ego often suffer from this trope.) Batman? Well, until a few decades ago, the one he would be constantly saving was his oft kidnapped sidekick, Robin: The Boy Hostage (aren't we all glad they toughened him up).
See the infamous image of the JLA being told that they have doomed their love interests... except that Batman doesn't have a love interest. He has Robin. Ho Yay indeed.
At least he was smart enough not to think of Robin's real name.
Batman sometimes has a Distressed Damsel love interest. Julie Madison and Vicki Vale in The Golden Age of Comic Books; Silver St. Cloud in the Seventies, and Jezebel Jet in the modern age. No, wait, scratch that last one...
Also subverted, in a different way, by Mary Jane Watson after her marriage to Peter. Whenever she's confronted by obsessive stalkers, she (almost) always manages to escape on her own, without any help from her super-powered husband. Even more subverted by the fact that, more often than not, Mary Jane is the one who bails out Spider-Man whenever one of his opponents has the upper hand in a fight.
Even before their marriage, when Mary Jane was witness to a Spidey fight going poorly, she'd often brazenly distract or sabotage the bad guy, relying on her charm and wit to save her from the dangerous consequences.
Even Aunt flippin' May has taken out bad guys. When (fairly) recently the Chameleon had assembled a group of Spider-Bad guys to go after Peter Parker (This is just before Civil War, natch) the Chameleon himself disguised himself as Peter to go and kidnap Aunt May. Aunt May opens the door, and lets her nephew in, and gives him some tea and biscuits while she has to finish her knitting before revealing that she drugged the fucking tea cause she'd recognize her beloved nephew anywhere and Chameleon obviously was an impostor, holding up "GOTCHA" written across the sweater she just made in aknitted moment of awesome.
Role-reversal: Yorick in Y: The Last Man is the spoilt "damsel" who has to be saved by the tougher and more experienced women around him, Action Girl 355 in particular.
However, Yorick sometimes has his moments, even in the beginning when he's useless most of the time. In one Crowning Moment of Awesome, Yorick is the prisoner of an Israeli commander who is about to shoot down a space shuttle with two live men on board. He attacks her from behind and ruins her shot. And then he knocks her out. Despite him being locked in handcuffs which not even an escape artist like himself can get out of.
Heather Hudson attempted to invert this trope in Alpha Flight, even referencing it. When she finds out her two-hour wait for her husband (Guardian) is a set-up, she tries to storm out: "Other wives and girlfriends may be content to play bait for the good guys, but I'm not going to stand around waiting for you to use me to lure Mac into your lair." But by then, Mac's been captured; they want revenge against Heather, too. (The woman with her throws her across the room.)
The main character of Empowered almost always ends up captured by villains, as a parody of Faux Action Girls. Naturally this leads to her being the laughingstock of the superhero community. Nonetheless, despite all the ridicule she receives and her general lack of success as a superheroine, she proves to be a Determinator who refuses to quit.
Most of the women in Sin City due to its Noir roots.
Subverted with Jadina from Les Légendaires; her typical Spoiled Sweet attitude, natural clumsyness and the fact she's a princess seems to make her designed for this role, and Danael even mentionned she has been this at least once; however, she never falls into that role, and actually is the one saving her friends most of the time, sometimes even doing so when weakened. This reaches its paroxysm in Book 14, where after she got temporary depowered and had her friends saving her, but still saves her friends from the new Big Bad Abyss, who none of her friend could even scratch. And all of this while still depowered. Wow.
April O'Neil from Teenage Mutant Ninja Turtles. In almost all of the TMNT continuities, she is a good friend of the Turtles, and is a love interest to Donatello in the 2012 cartoon. While it varies by incarnation, as the turtles' most prominent human friend she is often in need of rescue, particularly in the 1987 cartoon.
In Violine, Violine is regularly in need of saving, and occasionally tied up as well.