Howl's Moving Castle: Howl and Sophie meet when two soldiers hit on Sophie. Howl uses his magic to send them away. It gets better when Howl takes to the air in order to save both of them from the blob-men of the Witch of the Waste.
Rentarou meets Kishika, his seventeenth girlfriend, when she fights off some boys who were harassing him.
Used slightly in Ai Yori Aoshi, when Kaoru kicks Aoi out of his apartment, then goes to rescue her. No fight occurs though... Basically sums up as: "Come on, that innocent girl is part of some big conspiracy? What am I, a freakin' moron? Uh oh, creeps 3 o'clock..." In their defense, the creeps were remarkably good-natured about the whole thing: at no point did they offer to rearrange Kaoru's features over the incident, and even reprimanded him for his poor treatment of the girl.
Played with in Arakawa Under the Bridge. The story begins with Kou Ichinomiya being rescued from drowning by Nino, and being a Debt Detester he insists on repaying her somehow. So she basically proposes that he becomes her boyfriend and lives with her.
Mikasa's undying devotion and implied romantic feelings for Eren seem to stem from how he saved her life when they met. Mikasa's parents had just been murdered and she was at the mercy of the killers, then Eren showed up and killed them, and as a corollary, Eren's mother took Mikasa into the Yeager family.
Discussed by Shipper on Deck Reiner, when he teases(?) Bertolt by suggesting that rescuing his crush could result in her falling for him.
In Black Cat, Train happened to be visiting the same part of town as Kyoko. She gets attacked by thugs, and he decides to intervene, easily disarming all of them. Although she actually didn't need saving, this caused her to fall in love at first sight. She proceeds to become another Stalker with a Crush of his, though all of it is rather hopeless for her, considering his personality.
Played for Laughs in the anime. Yoruichi rescues Soifon causing her to completely melt and turn all googly-eyed and gushy.
This is how Isshin and Masaki met and got together. When Isshin interferes with Aizen's latest hollowfication experiment, Aizen sabotages Isshin's chances of killing the hollow, and as a result, Isshin is severely wounded. Masaki jumps in and kills the hollow, saving Isshin's life but inadvertently suffering a fatal hollow infection in the process. Isshin's decision to save her right back meant he had to sacrifice his shinigami power to do so.
One of Ichigo's strongest motivations is to protect his loved ones, and two of these persons are girls not related to him: Rukia, the Action Girl who gave him his powers at first, and Orihime, his Barrier Warrior friend. Each girl gets abducted for different reasons, and each time Ichigo pulls a Roaring Rampage of Rescue for her. The one he marries is Orihime.
Somewhat inverted in the anime Blood+. Though Haji does end up saving Saya during their "first" meeting (at least long enough to get her to save herself), she initially mistakes him for a serial killer and runs scared.
Done in B.O.D.Y, when Ryoko is saved from creepy guys on the street by Jin.
Invoked twice in Canaan. Maria Oosawa wants to replay her first meeting with the titular Action Girl, so she intentionally gets in trouble. Also, Liang Qi had set up a trap for Alphard to get captured in the beginning so that Liang Qi would get to rescue her. Alphard was very aware of this and went along merely because she was curious where Liang Qi was going with it.
Specifically invoked and then harshly deconstructed. A guy who hopelessly crushes on Ran, Sonoko, and Shinichi's sempai Asami drugs her when they go karaoke singing and then secretly sets her place on fire, hoping she'd finally fall for him when he rescued her. In the end, not only Ran was the one who really rescued Asami, but Conan (through Kogoro) revealed his gambit to everyone, harshly calling him out on his selfishness.
Played straighter with the Official Couple of Ran and Shinichi, since they've mutually helped and rescued each other (even if Shinichi is in his Conan form almost all the time) several times - often a great risk to themselves. Lampshaded once when Ran's drugged and almost forcibly drowned at some point, then Conan rushes in to help her; thanks to the drug and lack of oxygen she sees Conan as Shinichi, and before passing out she smiles and says "Don't worry, I'm okay... Shinichi came to save me..."
Played straight with Makoto and Sonoko when the former saved the latter from a serial killer, kickstarting their relationship in the process. He was attracted to her when he saw her cheer for Ran in a karate competition he was also in.
During an attack by the Graviton Bomber in A Certain Scientific Railgun, a random cop saves a girl from an explosion. Later, the gang runs into the two, and they are now dating.
Code Geass: Euphemia ends up on both sides of this trope.
She fakes being in danger after Suzaku catches her falling, to get him to spend the day with her.
Later, Nina falls for Euphie after Euphie rescues her from a hostage situation.
Played with in the BL manga Cool/Uncool by Kai Asou. The story is about how main characters Yukihisa (uke) and Takashi (seme), now best friends, get together, but Yukihisa gives backstory to their relationship by remembering their first meeting in elementary school, where Yukihisa is a bullied transfer student whose tormentors are Takashi's group of friends. When Yukihisa is eventually called out in a schoolyard fight, the manga seems to set up this trope when Yukihisa is put in a two-on-situation. When the reader turns the page, it ends up with Yukihisa kicking the asses of his bullies, and when Takashi arrives, supposedly to rescue him and thereby invoke this trope, Yukihisa ends up tacking him to the ground as if he were another bully.
Parodied in one episode of Daily Lives of High School Boys: the student council of the boys' school is talking with the girls' school's student council president, trying to get her to do them a favor. A man comes by and mistakes their conversation for thugs trying to hit on an unwilling girl, and tries to pull a classic Rescue Romance. Noticing this and deciding to "help", the guys immediately start pretending to be thugs and then deliberately fall easily. Sadly, the girl president is a moron and thinks that they want her to punch the guy out afterward.
In a more mundane yet even more significant example, Ichikawa keeps Yamada from possibly getting banned from their school library for eating there, using a book to cover her chocolate box and then grasping her hand as she's about to eat a piece just as the librarian was walking by. Yamada had already been slowly developing a crush on him up to this point, with this instance being framed as her fully embracing/realizing her feelings for Ichikawa from then on.
Episode 13 of DARLING in the FRANXX reveals that Hiro and Zero Two formed a Puppy Love version of this during their childhood when the former tried to help the latter escape to the outside world. This later becomes the basis of their actual romance when they recover their memories and apologize for their mistakes in Episode 15.
DearS: Takeya gains the romance of his Unwanted Harem by coming to their rescue, starting with saving Ren from being run over on a highway, and rescuing Miu from having fallen down a well.
Played with. Koyama doesn't outright rescue Akira, but he does throw her her knife so that she can defend herself from the giant animals that have cornered her. It's this incident that causes her to develop feelings for him.
Played straight when Akira saves Koyama from Ryuuchi's gang, who had kidnapped him and tied him naked to a bed in an attempt to frame Mitsuru (It Makes Sense in Context), which causes a Relationship Upgrade between the two of them.
Later chapters of D.N.Angel have hinted at a romance between Satoshi and Risa after he saves her from a deadly fall.
Earthchild: Reisuke meets, and falls in love with, Kareri after she saves him from being hit by a truck.
Parodied when Fujisawa "saves" Miz from her monstrous-looking manservant (she was screaming because the servant poured cold water on her instead of hot). Miz falls in love with him anyway and doesn't bother correcting him.
This is later played straight when Shayla Shayla falls for Makoto after he takes a shot from a power staff for her. And again, in the Sequel Series when Makoto saves Kauru from drowning.
In Flame of Recca, Recca and Yanagi meet in a 'saved from forceful advances' scenario. Played slightly more straight in the anime when Recca pushes her out of the way of a bunch of falling girders.
This is what kicks off the plot of Fly Me to the Moon - Tsukasa saves Nasa from being hit by a truck, and he falls head over heels in love with her.
Gloriously subverted in Fujimura-kun Mates. The titular character, Fujimura, once saved a girl from a group of delinquents. Then a very cute and grateful imouto character shows up at his school, initially assumed to be the girl he saved. Turns out, she's the leader of the delinquents!
Also played with in an episode of Full Metal Panic? Fumoffu: the karate club's strategy for a "flirting contest" involves dressing up three of its members as thugs and having them accost young women so that Tsubaki can come to their rescue. It backfires spectacularly when the crowd of girls he's "rescued" in this fashion find out it was for a contest.
Dancing Very Merry Christmas also subverts it when Tessa gets captured and Sousuke goes to retrieve her. The ensuing rescue fits all the associated action movie romance tropes so well that Tessa almost believes for a second that she might have won the Love Triangle as Sousuke jumps out of an exploding airplane to perform a Diving Save and (inadvertantly) kisses her ear as he catches her. Then she realizes that Sousuke decided to Shoot the Hostage Taker, a risk he's perfectly comfortable taking on anyone but Kaname. So to get over it as quickly as possible, Tessa asks Sousuke if he's in love with Kaname rather than her. He tersely answers yes.
Tessa: You just had to put that so bluntly, didn't you? Sousuke: ... Sorry.
Tamahome rescues Miaka from some pervy thugs at the beginning of Fushigi Yuugi. Nakago, bastard that he is, does the same with Yui after the fact, and only encourages the resulting emotional vulnerability.
This is sincerely attempted by the antagonist of the manga Ginen Shounen. Hero Matataki is fighting tennis star Koda for the love of Matataki's childhood friend Mirai, armed with photos that show the future. After failing to win Mirai's heart through the benefits of fame and wealth, and only partly succeeding by threatening her with the possibility that refusing him would lead to Matataki's predicted death, his final step is to use a pair of photos to save Mirai from certain death and have her wake up in his arms, at which point he's certain she'll fall in love with him. Subverted here though, as this has no effect on Mirai's feelings: she's still willing to marry Koda without hesitation, but only because she thinks it's necessary to protect Matataki, and realizing this fact is what finally wakes Koda up.
This is what kicks off the plot of Gonin Hitoyaku demo Kimi ga Suki. Taiga falls in love with Chika after she saves him from the manure pit he fell into, then discovers that she's actually a fake identity assumed by five quintuplet sisters and decides to make them all his girlfriends due to being unable to tell just which girl he fell in love with.
In Guardian Fairy Michel, Salome tries to invoke this in one episode in the hopes of getting some treasure.
Both played straight and played with in GUN×SWORD. Van and Wendy meet when he rescues her, but he wasn't trying to rescue her; apparently, he thought she was already dead. Later in the same episode, he deliberately chooses to rescue her, despite having turned down her offer of marriage.
Subverted in Gundam Wing's Episode Zero manga, where Middie Une falls in love with No-name aka the future Trowa Barton after he rescues and recruits her into their mercenary group, but she still betrays the band to protect and feed her family.
Gunslinger Girl: Cyborg girl Triela has her Love Epiphany when she discovers that not only did her handler Victor Hilshire save her from a Snuff Film, but he became her handler solely to continue protecting her. Then it's subverted because she doesn't pursue him. Triela is Genre Savvy enough to realize that a good part of her feelings may come from her conditioning and that a man like Hilshire is not interested in romance with his 14-year-old Protectorate.
In the h-mangaHands-On Draining with Three Succubus Sisters, the three Amaki sisters have the reputation of being the most beautiful girls in school, but are also known to have ice cold personalities as they tell anyone who talks to them to get away and not touch them. The reason being is because they are succubi that are trying to survive in the human world without being discovered, and while Lemy, the eldest sister has accepted her faith of not being able to touch a person without giving them an orgasm that could kill a human, Lamy, the second eldest, has a brief nervous down at the realization that she'll never lead a normal life since she'll never experience love, or even friendship without risking killing the other person, and even if the other pserson survives being touchedm their memories will have to be erased. Just then, Yuuki Suruga unknowingly shakes her hand and when he shows no ill effects, she decides to follow him with the intent of befriending him. When Lamy sees him getting beat up by some girls who frequently bully him, she touches the girls and tells Yuuki she saved him, and when she confirms that he can touch her without sideffects, she immediately makes him her boyfriend and uses him to take out her pent up frustrations.
Hayate and Nagi meet in a similar 'saved from thugs' fashion; unknown to Nagi, Hayate's original intention was to kidnap her - he was protecting his prey...Hayate is almost instantly regretful of his intentions, though.
Hayate ends up saving a lot of the series' girls this way, and even a guy at one point—though that one didn't create any romantic undertones.
Hello! Sandybell: Despite their rough start, Kitty falls for Alec when he saves her and Sandybell from mortal danger.
Highschool of the Dead: Asami fell hard for Hirano after he stood up to Shimada for her, to keep him from raping Shizuka. Shortly after the incident, she followed him up to the rooftop to thank him, while dropping not-so-subtle hints that she was availableand interested.
Satoshi Hojou saves Shion Sonozaki from a group of thugs in a flashback in Higurashi: When They Cry (the same thugs who have also tried to attack Keiichi Maehara, Rika Furude, and Satoshi's sister Satoko in different timelines). This leads to Shion immediately falling in love with Satoshi. However, as this is Higurashi, her love isa bitdifferent. (Only in two worlds, to be fair.)
Gender inverted in the anime. Sonsaku Hakufu used to protect her cousin Shuuyu Koukin from bullies when they were small, and Koukin fell in love with Hakufu when they grew up.
This is how Jinenji's parents met decades ago. Jinenji's mother was a villager girl who once hurt her leg when collecting herbs, and was rescued by a kind youkai.
There are all the instances in which Inuyasha and Kagome rescue each other throughout the whole story, starting with Kagome unsealing Inuyasha from the tree that Kikyou pinned him against so he can fight off the Centipede Woman about to kill her. It even got lampshaded at the start, when Kagome talked her way out of the Thunder Brothers killing her via making them believe that Inuyasha was her boyfriend and would come for her later so it was not in their best interests to murder her.
Occasionally happens between Miroku and Sango as well.
In K, Shiro is running away from HOMRA in the first episode when Kuroh saves him. Kuroh picks Shiro up in his arms, and Shiro blushes as he sees Kuroh's face for the first time. Then Kuroh carries him up to a rooftop... and proceeds to try to "slay" Shiro himself. They do end up being teammates, though, with a lot more romantic moments later on - and Kuroh does stop trying to slay him.
Kindergarten Wars: Doug, the series' male lead, develops feelings for Rita, the main protagonist, after she saves him from assassins. Likewise, Hana falls for Doug after he saves her from rubble. And on top of that, Natsuki falls for Hana when she saves him from a collapsing building. Are you starting to see a pattern here?
La Seine No Hoshi falls for Black Tulip after he aids her in battle, though he's obviously Richard de Forges in disguise.
Lovely★Complex: Seiko falls for Otani after Otani saves her from a dog.
The first meeting of Subaru and Ixpellia in StrikerS Sound Stage X began with Subaru shielding Ix from falling debris, followed by Subaru fighting off the Mariages that came for Ix (with an accompanying image of a very battered Subaru cradling Ix as they gaze into each other's eyes), and ended with Subaru symbolically and literally bringing Ix out of the darkness and into the light of the current era. When all of that was done, Ix saw Subaru as one of the only people she felt calm with because she rescued her. Unsurprisingly, there's a small but noticeable amount of supporters for this ship which would have been bigger, had Ix not entered her 1000 years of sleep.
And for a straighter example in both senses of the phrase, we have Tohma and Lily, the main pairing for Force who first meet when Tohma finds Lily bound in an abandoned lab, releases her, and takes her with him.
And, of course, more or less the basis for Fate/Nanoha. Nanoha is the one who helps her through her ordeals, after all.
The Nanoha and Fate Rescue Romance gets reversed in Magical Girl Lyrical Nanoha INNOCENT, with Nanoha meeting Fate for the first time when the latter saves the former from getting hammered by Vita. This was given a Lampshade Hanging by Arisa as she teased Nanoha about her obvious developing crush on Fate.
Discussed and deconstructed in an episode of Magical Pokaan, where the girls are discussing how they would like to meet their future boyfriends. Liru suggests this as her preferred scenario, but Aiko criticizes her, saying that such relationships tend to be based on heat-of-the-moment attraction and don't tend to last.
Maris the Chojo: Invoked. Whilst Maris has to save intergalactic heir Koganemaru as part of her job, she is also excited by the idea that he may fall in love with her for rescuing him and propose to her. At least partially because she hopes that marrying a billionaire will help her escape her Perpetual Poverty.
MARRIAGETOXIN: Invoked in the premise. Protagonist Gero is an assassin that wants to find a wife to continue his clan, however, he has no social skills, relatable interests, and no capacity to charm someone when actually interacting with them. Kinosaki, a marriage swindler whose helps he enlists, realizes he is at his most charming when he is rescuing or fighting to protect people, prompting him to take up jobs which involves rescuing and bodyguarding women to show his best side to possible romantic interests.
Luna in the Mega Man Star Force anime - Megaman saves her from falling to her death, and overnight she becomes a (non-evil) Stalker with a Crush. Happens to a lesser degree in the game.
Mermaid Melody Pichi Pichi Pitch, based on the original "The Little Mermaid" story, has two Rescue Romances, both involving the same person and causing a rivalry that lasts the second season. Interestingly, Lucia saved Kaito from drowning when they were six, and Kaito does the "chase away perverts" variant multiple times in the story, but the former is more important to their relationship than the latter.
Seiji Sawamura saves Takako Ayase in Midori Days from a band of delinquents that were dragging her away. She falls in love shortly afterward when she sees him letting himself get beaten up without resorting to violence (fighting back) in order to save a friend and defuse the gang's grudge.
Mission: Yozakura Family: Ayaka falls in love with Mutsumi after the latter saves her from an assassin.
Tohru has been in love with Kobayashi ever since she pulled a holy sword out of her back. Although her feelings are unrequited due to Incompatible Orientation.
It happens again with Ilulu when Kobayashi stands up to a Knights Templar Order dragon to protect her. Her feelings are also unrequited, resulting in her redirecting her feelings to Taketo instead.
Mobile Suit Victory Gundam has a very twisted example on the antagonists side when Katejina Loos falls for Chronocle Asher when he saves her from getting raped. By the end of the series, she's gone from a Jerk with a Heart of Gold to a murderous lunatic, and it's unclear how much of it is his fault.
Played with repeatedly. Tenma's first meeting with adult Nina when she's waiting by Heidelberg castle seems like it's going this way, except for the aversion they never unambiguously get beyond Will They or Won't They?, the inversion she ends up rescuing him that time, and by being there, they both fail to save her foster parents, and the disturbing subversion that her Meet Cute-ish Lampshade Hanging response to Tenma's appearance ("Are you my prince?") is primed by a series of anonymous romantic emails which are actually from her twin brother..
In a more straightforward(!) subversion, both the Big Bad and The Dragon frequently pose as rescuers and unexpected friends and allies, romantically or otherwise, in order to further their plans. Karl's quasi-idolatrous friendship with Johan also just keeps on giving on the Dramatic Irony and Fridge Horror fronts, the more you find out about Karl's family and Johan's connections with them.
Johan's own Mind Game Ship fixation on Tenma could also be seen as a very warped one-sided version of this, for all Johan's questionable reassurance that he sees Tenma as a father figure since Tenma saved his life when he was a very young boy.
Also by way of subversion, Tenma's repeated rescues of his Stalker with a Crush ex Eva who eventually gets the nearest to straight version of this trope with her bodyguard Martin, and Nina's response to Tenma saving her brother.
Averted when Nina is rescued and nursed back to health by Lipsky. He develops feelings for her, but she doesn't seem to view him as anything more than a close friend.
Played with in My Bride is a Mermaid. Nagasumi and Sun first met when she saved him from drowning, but they don't fall in love until later in the story.
Satori plays this straight when she falls in love with Nagasumi after he saves her from a collapsing theatre.
Maruko also falls for Nagasumi after he saves her life.
My Hero Academia plays it both ways with Izuku Midoriya and Ochaco Uraraka. During the entry exam for the UA High, Ochaco ends up with her leg pinned by some debris as a giant robot approaches. Disregarding his own safety and the fact that he needs to score points, Izuku rushes to jump in and smashes the robot with a single punch to save her. Unfortunately, the strain of using his powers ends up leaving his limbs crippled and he plummets to the ground, but then Ochaco uses her zero-gravity powers to stop him before he hits the ground, saving him as well. As the story advances, it becomes evident that the two have developed feelings for each other, but they both are too shy to express them.
My Love Story!! starts when Takeo saves Yamato from a man on the train. It's Love at First Sight and they start dating soon afterwards, though Takeo at first thinks that Yamato would fall for his best friend. Later it turns out he had met Yamato years before.
Rock Lee believes in this with Sakura. Despite her unwavering love for Sasuke, Sakura appreciates and respects Lee's efforts in protecting her.
Double Subverted in Chapter 437, when Hinata jumps in to try to save Naruto from Pain. She tells Naruto that she can't stay back while he's in danger because she loves him, then attacks Pain — who, after a brief fight, smacks her down, stabs her, and insinuates to Naruto that she's dead. Naruto promptly loses it worse than he ever has before. The anime not only extends the fight but also turns it into a Meaningful Echo with both characters in the opposite positions when they were younger, against a trio of bullies; this was later canonized in The Last: Naruto the Movie. They play this straight in The Last. Now adults, Naruto again saves Hinata, this time from Toneri, and after the Final Battle, they finally begin their romantic relationship—it serves as a Call-Back and Meaningful Echo to the story of how Naruto's parents fell in love.
As revealed in Chapter 498, Naruto's mother, Kushina, fell in love with Naruto's father, Minato, when he saved her from the Kumo ninja that kidnapped her when she was a kid, and then boldly complimented her red hair, which other children used as a reason to bully her.
As revealed in Chapter 482, Karin fell in love with Sasuke after he saved her from a bear in a Chuunin exam she was taking.
Also spoofed in Episode 101 of the original anime. In a flashback, Kakashi easily defeats the pathetic Moya Triad who had been pestering a random woman, and afterwards she's completely smitten with Kakashi.
Rin also loved Kakashi before and after he rescued her, even jumping in front of his attack so that the tailed beast inside her couldn't be unleashed—this was her idea of a "rescue".
Given Setsuna's obvious Bodyguard Crush on Konoka and Konoka's reaction every time "Secchan" saves her, this forms much of the basis behind the casual observer's view of them. When they finally pactio (and Konoka seems to be hinting broadly that it's gone from subtext to text) in Chapter 252, it happens immediately after Setsuna saved Konoka without even realizing it.
Lampshaded early on in Chapter 55 when the girls think Negi is going to confess to Ku Fei as a result of her saving him that morning.
Negi's first major interaction with Nodoka involved catching her after she fell off of a staircase, and he saved her from Evangeline not long after. When he saves her in Chapter 219 from a group of bounty hunters, he goes half-nuts on them when he sees what they're doing to her. They have a pretty serious moment in Chapter 228 after she rescues him, at least until Kotarou jumps in. She also rescues him earlier on in Chapter 41, helping him win his first fight with Kotaro. A good chunk of their relationship consists of saving each other's asses.
Negi's father Nagi and Negi's Tsundere mother Arikafinallykiss right after he and his friends rescue her from being unfairly executed on (fake) charges of treason and genocide in Chapter 269.
Deconstructed in Neon Genesis Evangelion, where Shinji jumps into the Mount Asama volcano, without protective gear, on the off-chance he can get Asuka out of it in time. Asuka, due to her pride and troubled past, simultaneously wants Shinji to accept her feelings and not feel dependent on him, leading to tension between them.
One Piece Oda's stand on No Hugging, No Kissing makes sure the "romance" part of the rescue is underplayed or not there at all, but there some notable cases...
Kohza and Vivi as children, leaving her feelings towards him as more than platonic.
Sanji always tries this with Nami after his Big Entrance (often sending the bad guy flying), Sanji will turn to her ask Have you fallen in love with me now? she gives him varying responses: telling him to go blow off, saying she loves him so that he will hurry up, or actually being genuinely grateful for the rescue.
Combined with Bodyguard Crush in the Dressrosa arc In a flashback showing the past of the Thunder Soldier shows he was the bodyguard of Rebecca's mother, who disliked him because of his criminal past until he rescued her from a kidnapping attempt.
In episode 9 of Osomatsu-san Jyushimatsu practices his baseball swing on the beach when he spots a woman ready to jump off a cliff. He decides to keep swinging until she gets away from the edge, but Jyushimatsu ends up engulfed by water. The unnamed woman ultimately ends up saving him.
The normally strong-willed Haruhi from Ouran High School Host Club is unapproachable to the host club's cliched attempts at romantic talk. However, she's terrified to the point of cowering in the fetal position at the sound of thunder. Two of the male cast get closer to her by saving her from this.
Done twice at the end of the anime when Haruhi chases down Tamaki in a horse-drawn carriage to stop him from leaving the Host Club and his happiness. Then when she holds out her hand to reach for him, the carriage tumbles and the poor girl goes flying off the bridge... leading Tamaki to jump out of the car and rescue her.
Invoked intentionally in Penguindrum, when Ringo tries to stage an incident where she's drowning so her crush Tabuki will rescue her. Subverted since it fails, so Shoma has to save her. And then it's played straight because, after settling her thoughts on Tabuki, Ringo falls for Shouma instead.
In Persona 4: The Animation, Rise falls in love with Yu after he saves her life. While the rest of the team helped to rescue her, she developed an intense attraction towards him alone. This might possibly be due to the fact that during Rise's first appearance in the mall scene, she believes someone is chasing her, until she's trapped and learns that Yu simply wanted to return her phone to her, then leaving, without making any indication that he knows who she is. This may have led her to believe there was a Recognition Failure.
Phantom Quest Corp.: Though it's implied that Makiko met Bosco through his teashop, and had secretly been allowing him to feed on her, she doesn't fall for him until he helps save her from Dracula. They become an Official Couple at the conclusion of the first Incident File.
Ash's first major opponent in the Johto League, Macy, suggests this in a not-very-subtle way after he saves her and her Vulpix during a Team Rocket attack. Ash being Ash, this does not go anywhere.
Ash saves Misty a few times, and while Ash was oblivious, it very much meant something to Misty
Also part of the backstory of Serena, part of Ash's Kalos band of True Companions. When they were both little, he rescued her from being lost in a forest. A recent incident that helped jog her memory of the event would drive her to find him and join his group.
Parodied with a girl who falls in love with three different guys who "save" her in relatively minor ways—one of whom is Brock, who's thrown completely off his game and doesn't recover until she's moved on to the next guy—James.
Almost played straight (or at least fantasized about) by Jessie when a guest doctor rescues her, to the point where she's willing to leave Team Rocket. However, he's already in love with someone else, so she decides to let them be together.
The relationship between Professors Kukui and Burnet has shades of this, as they get married a few episodes after Kukui and his Braviary save Burnet from a Zerg Rush of Dragon Pokémon.
Heavily implied in Pokémon Heroes between Ash and Latias, the two get plenty of Ship Tease with Latias clearly crushing on Ash and their first major interaction was when Ash saved her from Annie and Oakley, of course aside from a kiss on the cheek nothing ever comes from it.
Zig-Zagging Trope in Pokémon: The Rise of Darkrai between Alice and Tonio. When they were children, Alice believed that Tonio had saved her from falling off a cliff and professed her love right then and there. Tonio admits during the course of the movie that he didn't know what had really saved her, but has just realized that it was the Pokémon Darkrai, leaving Alice at least mildly disappointed. During the climactic battle, Tonio saves Alice for real, and her reaction shows that the romance is back on track.
In Pokémon Adventures, Yellow both gains admiration for and falls in love with Red after he saves her life from a rampaging Dratini, prompting her to be determined to save ''him'' when she learns that he's gone missing. Of course, Red, being as oblivious as he is, doesn't recognize her as the girl he once saved and probably never bothered wondering why she went through so much trouble for him.
Parodied. Sakuno has a crush on Ryoma from the first time she saw him when he stopped a show-off who was about to hit her on the face with his racket - but it turns out Ryoma had not even acknowledged Sakuno's presence back then, and only stopped the moron because he was too loud and didn't let him nap in the train.
Arguably played a bit more straight with An and Momoshiro: he saved her and Sakuno from bullies first, later he teamed up with Kamio to have Atobe give up on forcing her on a date. Arguably, because neither Momo nor An make moves towards a Relationship Upgrade when given the chance (despite the relationship chart hinting at her having a crush on him), whereas Kamio is firmly put in the role of the Unlucky Childhood Friend.
In the first episode, Princess Tutu saves Mytho after he jumps out a window to save a baby bird from a raven attack. She then starts to save him about Once per Episode until he starts to fall for her.
Also, it's revealed in the second season that Rue met Mytho when he saved her from a crow attack, and she in turn saved his life by giving him water through a kiss. Fakir might count for Mytho, as well. Also Ahiru and Fakir's most romantic scenes come when they are rescuing each other.
And by the end, Rue and Mytho fully seal the trope when they rescue each other. On one hand, Rue's Anguished Declaration of Love breaks the spell that has turned Mytho evil (which she mistakenly helped cause one might add), and when Tutu arrives next to a now-normal Mytho she tells him that Rue saved him. On the other hand, Rue is immediately captured by her Archnemesis Dad the Raven, and Mytho rescues her from a slow and agonizing death.
The Quintessential Quintuplets: Nino's relationship with Fuutarou starts out as antagonistic, but she gradually falls for him throughout several incidents that could be construed as this trope. In the early chapters, she shields her from a stack of falling books and during the fireworks festival manages to pull her out of a jostling crowd before she gets lost. Later during the school trip, while dressed as "Kintarou", he finds her alone and scared in the forest and saves her from falling off a cliff when she runs off blindly. And much later, at one point that Fuutarou falls into a lake, she and her sisters jump into the water to save him but since she can't swim, ends up having to be rescued by him instead. The one that seals the deal happens in Chapter 59 when she's having an argument with her father over whether she and the others should keep staying at their current place or not, and Fuutarou shows up on a motorbike and takes her away, prompting her to confess that she's fallen in love with him.
Averted in Ranma ½: Ranma Saotome saves Kodachi Kuno from falling off of a roof — but caused her to fall in the first place because he accidentally hit her in the head while she was running away from an attempt to ambush Akane Tendo. Kodachi fixates him on a romantic figure after she comes to, but Ranma does not reciprocate her feelings, due to a combination of having two existing Arranged Marriages (though he's only aware of one at the moment) and an Accidental Marriage (though neither he nor the girl in question is aware of it at this precise moment), and Kodachi's... unusual... ideas about romance. Her first action after regaining consciousness — well, second, her first is to cuddle to him and ask for his name — is to paralyze him with a bouquet of poison-laced roses so she can kiss him.
While Utena at first mostly intended to duel Saionji for being cruel to Wakaba, winning their duel let her 'win' another girl he mistreats: Anthy, the Rose Bride. Whom she protects from anyone who wants to possess and harm her, including her once-kind-and-now-abusive brother and the Big Bad, Akio. And including HERSELF, in a sense, since she did it more in self-interest than to genuinely help Anthy. And it turns out this was a sort-of Invoked Trope since Akio was so smart that he arranged for Anthy to be in vulnerable positions to fire up Utena's Bully Hunter side and bring her into the duels. She's devastated when she finds out, then realises that she also was selfish to Anthy and resolves to truly aid her.
Spun around quite a bit in the case of Tsuwabuki and Nanami. Tsuwabuki has this big-ass Precocious Crush on Nanami and wants to help and protect her, right? Well, what's better than actually putting her in dangerous situations so he can rescue her, right?
Subverted in School Rumble - the entire reason Harima grew facial hair, wears sunglasses, and became a delinquent was so that he could be close to Tenma without her recognizing him. He fell in love with her after saving her from hoodlums, and took her back to his place because she was unconscious. When he leaned in for the traditional kiss, she woke up and thought he was about to molest her (or already had).
Subverted in Slayers: In the first episode of the anime adaptation, Gourry steps in to save Lina from Bandits, but she really didn't need the help. Also, while she does admit he's handsome and lets him continue traveling with her, the development of their relationship has more to do with their adventures together than their initial meeting (despite him having a Bodyguard Crush on her for quite a while).
This shows up mildly in the various Tenchi Muyo! continuities. In the manga, this ends up turned on its ear when Aeka waits for her saviour after being captured, hoping for a little Rescue Romance with Tenchi ... and finds Ryoko coming to the rescue (she knocked Tenchi out and took the only available spaceship so that he wouldn't be able to put himself at risk). Aeka's disappointed in the choice of rescuer, and Ryoko isn't very fond of the lack of gratitude. Resulting in Ryoko Dope Slaping Aeka so hard she feels it even through the force field that confines her.
Kotetsu Kaburagi and Tomoe Amamiya's relationship was kick-started when Kotetsu rescued her from a factory explosion. Of course, the fact that he was an aspiring superhero and she was a raging superhero fangirl might have had something to do with it.
The details aren't given to the reader, but Takuma saved Natsuki when they first met and she is clearly in love with him.
Misa falls in love with Takuma after he rescues her soul from falling into Hell.
The Vision of Escaflowne has something of a mutual Rescue Romance: Van starts falling in love with Hitomi after she pulls a Diving Save on him in episode 6, saving him from being impaled by Dilandau. Meanwhile, Hitomi begins seeing Van as something beyond "that guy I'm tagging along with until I can get back home" after he saves her from a kidnapping attempt (rather than the expected Knight in Shining Armor, Allen) in the subsequent episode.
In Waratte! Sotomura-san, Sotomura's parents met when her mother saved her father from delinquents. Sotomura believes it was the other way around.
In Wild Rock, the first time Yuuen and Emba meet Yuuen is about to be killed by a giant sabre-toothed animal he had been trying to hunt. Emba flies in out of nowhere and stabs it in the neck and promptly tells Yuuen he's incapable of wielding a weapon. The others get riled up over this but Yuuen is just grateful to have been saved. Emba also gets injured rescuing him from a giant alligator later on. The trope is not quite played straight with their fathers, where it was Selim's own hunting trap that he had to save Yuni from.
Doumeki saves Watanuki too many times to count in ×××HOLiC. Ho Yay ensues, at least for the fans.
In Yu-Gi-Oh!, Tea falls in love with Yami after he saves her from being held hostage. However, she's blindfolded at the time, so she only hears his voice and doesn't know that Yami is Yugi's Superpowered Evil Side. When she finds out, their relationship gets...complicated.
In Yuuna and the Haunted Hot Springs, Hibari falls in love with Kogarashi when he saves her from two male spirit ability users who were harassing her and were going to force her to marry one of them.
