Samaritan Relationship Starter

So Alice and Bob don't know each other yet, or Alice regards Bob with either indifference or dislike. But then, she witnesses him committing -- or becomes the recipient of -- some single act of kindness (rescuing someone from bullies, stopping to help someone with errands, etc.) that makes her think "maybe he's not so bad after all", causes her to develop a blossoming crush on him, or otherwise shoehorns the two towards a romantic relationship.

Psychology-wise, the trope works due to the belief on the part of the girl that only she has seen this "hidden side" of the guy, which makes her feel special and connected with him. Dangerously Genre Savvy characters can exploit this.

Essentially, a form of Relationship Upgrade that tends to happen very early on in the Romance Arc, if not start it entirely. Rescue Romance and Returning the Handkerchief are particularly common types of Samaritan Relationship Starter.

Anime and Manga

 * When Shinji defeats the Angel in his first fight together with Asuka in Neon Genesis Evangelion.
 * Even more so when he saves her from death by volcano by jumping into the lava without any sort of protective equipment.
 * On the other hand, this eventually gets inverted: Asuka becomes allergic to anyone demonstrating kindness to her, deliberately mistaking their genuine intentions towards her as pity.
 * In Ratman, the Rebellious Princess character already kind of likes the hero, though she thinks of him as a wimpy kid who needs protection. Then she sees him rescue a kitten from being run over (without the benefit of superpowers) and she immediately upgrades her opinion to "has a hero's heart"--especially significant as the "real" professional heroes ignored the situation.
 * Hayate of Hayate the Combat Butler saves Nagi from kidnappers, which kickstarts their relationship.
 * In Midori Days, it's this trope, not Rescue Romance, that kickstarts Takako Ayase's crush towards Seiji Sawamura. Seiji does catch her attention after he rescues her from school delinquents, but she's still wary of him because she still believes he's a blood-thirsty fight seeker. It's only after witnessing Sawamura deliberately taking a beating without retaliating in order to save a friend and to defuse the hate the Delinquents have for him, that she falls in love with him.
 * Invoked in The World God Only Knows for the middle school girl's capture, which is mostly told from her perspective. Keima fakes being a member of the swim team and pretends to do really well and looks cool. When he disappears, she builds up a false impression of him as a really cool upperclassman (he calls it a free love potion to be a sempai), which balances against his bad reputation and has her develop a crush on him.
 * In Wild Rock, Yuni falls into an animal trap set by Selim. Selim gets him out and gently nurses him back to health. Since they're of rival clans, Yuni wouldn't have given him the time of day before this.
 * In Code Geass, Shirley thinks Lelouch is a cold, spoiled brat until she witnesses him helping out some strangers when no one else would. Thus begins her infamous and tragic crush on him.

Film

 * In Outlander, Freya reconsiders her opinion of Kainen after hearing how his valor in the fight against the bear saved her father's life.
 * Deliciously played with in Red Eye, which sort-of resembles a romantic comedy in the very beginning, before turning all creepy.
 * The Hunchback of Notre Dame - Phoebus is attracted to Esmerelda from the get-go (as is basically every main character), but once he sees her stand up to Frollo and his guards to protect Quasimodo, it's definite. Esmerelda initially sees him as just another one of Frollo's mooks, but that changes for similar reasons.

Live Action Television

 * This is what kickstarts the Will They or Won't They? for Barney and Robin in How I Met Your Mother, when Barney comforts Robin after she is dumped by a jerk boyfriend. They end up sleeping together, which leads to Barney realising he is in love with Robin.

Religion and Mythology

 * The Bible provides a variant: when Abraham's servant Eliezer is sent on a journey to find a wife for Isaac, he decides to pick the first woman who, when asked for a drink, offers to draw water for his camels as well. Given how physically exhausting it was to lug water out of a well for so many animals, the point was to pick a woman willing to go out of her way to help anyone in need.

Video Games

 * In the Neverwinter Nights mod The Aielund Saga, Criosa really starts to consider the male player character in this manner if you take the heroic dialogue options when helping out the dwarves at the start of chapter 3.

Western Animation

 * The Spectacular Spider-Man, Season 2: Jerk Jock Flash Thompson tries to hook up with quiet and artistic Sha Shan, completely failing to woo her when he relies on his usual sports reputation and personality to attract her attention. She only begins to respond to his affections when he reports to his coach that one of his teammates was using performance-enhancing drugs during their recent championship game. His actions force the team to retroactivel forfeit the game and lose their title, something that he had worked long and hard for, but he felt that the championship did not mean anything if had been earned dishonestly. After this, Sha begins to reciprocate his feelings.
 * In Total Drama Island, Courtney finds out that Duncan is a Jerk with a Heart of Gold when she sees him tricking DJ with a replacement Bunny so DJ wouldn't be sad.