Back in the day, it was not seen as kosher for a young woman to be seen in public with a man who was not a family member. One exception was during a rainy day, when a man could offer to share his umbrella with a young maiden in the street if she hadn't one herself.
It is a romantic image in media all over the world — but it doesn't quite have the iconic "oomph" to Westerners that it does in Japan. The Japanese equivalent of the 'John [arrow through heart] Jane' love graffiti is drawing the pair's names standing under an umbrella.
Compare Parasol of Prettiness, Old-Fashioned Rowboat Date.
It has a magical umbrella which makes any two people who share it fall in love. (Is any item in that series not magical?).
A "chapter title" illustration from the manga shows Ryoga and Akari standing happily under Ryoga's umbrella in a deliberate use of the trope.
One chapter title one had female-Ranma cheerfully whacking Ryouga to the ground with it.
The "carving one's names on a tree, under an umbrella-shaped symbol" version is used several times, especially by Kuno (to Ranma's annoyance, especially when the tree took it seriously,) but Genma and Nodoka did this too when they were dating.
The song "November Rain" from one of the albums is about a rather sad, subverted version of this trope. The entire reason why Ranma is singing the song is because he's heartbroken over his fiancée, Akane, ditching him under the umbrella they were sharing with each other. Since him hurting her feelings was what caused her to leave, he laments throughout the song over how he just can't seem to be tender with her.
Ranma: Even rain that's about to freeze from cold is warmer than my heart. November rain, until my tears vanish, don't stop.
In a bonus chapter of Vampire Knight, teenage Juuri Kuran walks home from a human school in the rain even though Haruka showed up at her school with an umbrella. They both end up getting drenched since he shuts his umbrella when it is obvious she is too irritated with him for hiding all the umbrellas in their mansion earlier that day by storming ahead of Haruka in a huff. When Juuri asks why he did such a childish thing after ranting at him for several minutes, he simply replies, "I wanted to share an umbrella with you."
It has a whole episode devoted to Kanade setting up sharing an umbrella for her and Yukino.
Yuki is really excited with the idea of sharing an umbrella with Kanade. It's both hilarious and heartwarming.
Maria-sama Ga Miteru has the episode "Holding a Parasol". It ends with a picture of Yumi and Sachiko sharing an umbrella under the sun.
Hayate and Vita of Magical Girl Lyrical Nanoha share an umbrella under the sun in the supplementary manga. And just to further drive up the Les Yay of the moment, Hayate gently caresses the blushing Vita while they talk about how it would be wonderful if they could be together always.
Kyouka from Kyouran Kazoku Nikki is probably one of the few people to pull off the Umbrella of Togetherness indoors. That's how much she wants to share a romantic moment.
×××HOLiC has a situation where Watanuki doesn't want to walk under one with Doumeki (whom he's an Unknown Rival of) because they're both guys and he has this trope in mind. This is just one of many Ho Yay moments between them. (It is a CLAMP manga after all...)
Greece and Japan share an umbrella, implying the image of lovers.
Japan's partner Italy uses the umbrella symbol in a poster, drawing himself and Germany underneath it without really understanding what it means.
Takahata's Only Yesterday when Teako decides to stay at the farm instead of going back to city, followed by ghost-like (yet charming) visions of herself and her classmates. She meets with Toshio, and as they walk side by side, the children construct a wooden 'together umbrella' and follow them with it to assure the audience that the two will get together and have a happy future.
In the manga, Mikan's parents have the umbrella scene in the Special Abilities room. Cue everybody from Special Abilities and some not getting their names added to the umbrella, with Mikan (unknowingly) writing herself as the child of her actual parents.
Such a scene appeared in Midori Days as not-so-subtle foreshadowing that Midori's feelings would not go unrequited for long.
In Doraemon, socially inept Nobita and his love interest Shizuka share an umbrella once.
In one episode of Samurai Champloo, Jin's Girl of the Week ends up sharing her umbrella with him when he gets stuck in a heavy downpour without one. And it is implied that he'll come back for her when her mandatory time on the island has ended, so there's hope for the "togetherness" part.
In 5 Centimeters per Second, the umbrella symbol shows up on a chalkboard with Akari and Takaki's names under it. When they see it, Akari looks embarassed while Takaki hastily erases it, implying that some other kids had drawn it.
In the anime, we have a scene where Yuki offers his umbrella to Tohru on the way home from school, much to Kyo's dismay.
In the manga, Tohru offers her umbrella to Kyo, since (as the Cat) he's utterly miserable in the rain. He gets flustered and angry, and turns her down.
Paranoia Agent: Drawing of lovers' umbrella symbol is briefly glimpsed in Ikari's dream world, drawn on a door in a school.
In the seventh episode of Pokémon, "The School of Hard Knocks", in the corner of Kaito's picture of Giselle, their names are written under the umbrella in kanji. 4Kids edited out the easter egg, obviously, because anything remotely Japanese or romantic is evil.
Done once in a Inuyasha episode. Miroku's hat had broken and he was left in the rain. Kagome gave Sango her spare umbrella and Sango shared the umbrella with Miroku.
In the 10th ending credits to Naruto Shippudden (the beach ending), we see at the end that Sakura and Sasuke's names are written under the umbrella symbol... only to be washed away by a passing wave.
When Hayate of Hayate the Combat Butler is kicked out of the Sanzenin mansion for three days, he's left sitting in the falling snow. Hinagiku finds him and shields him with her umbrella while they talk and she even invites him to warm up at her place.
Tsuda and Shino from Seitokai Yakuindomo walk home this way once. They're aware that they look like a couple doing that, and so is the school Camera Fiend not far behind them.
Non-romantic (or isit?) example: Durarara!! has a flashback with Berserker Shizuo Heiwajima standing in the rain by the jail after being set up for a crime, feeling and looking completely alone. Off screen, we hear a voice calling his name. It's a very close friend he lost contact with, who then holds his umbrella up over Shizuo's head as they walk off together. This is the anime version of Tom Tanaka's defining character moment, as he's been there for Shizuo ever since.
Played with in Code Geass for Lelouch and Shirley'sFirst Kiss. While going to meet her, he sees her standing in the rain and tries to hold the umbrella over her, but a combination of the shocking thing she tells him plus his surprise when she embraces him causes him to drop the umbrella, so they end up kissing in the rain.
A romantic scene with an umbrella happens off-screen between Yukari and Kouichi in Another. Not that it matters a lot, since said umbrella ends up giving Yukari an Impromptu Tracheotomy few moments afterwards.
In Yumekui Merry, there is such an umbrella drawn on the wall of the old playground, with Yumeji and Isana names.
Invoked in Campione!, when Erica snaps her umbrella in half while it was raining so that she has a chance to share an umbrella with her special someone.
In The Garden Of Words, a high school student is walking through a park in the rain when he comes across an older woman sheltering under a gazebo. As it's the start of the rainy season, this happens regularly over the next few months. By the time summer happens, they keep hoping for rain so they'll have an excuse to keep meeting each other.
In Sachiare!, Sachiko and Tomoharu's height difference makes it difficult for both to keep dry under one umbrella... so he picks her up and carries her. It's adorable.
Painting◊ Little Red Umbrella (The Lovers) by Josef Manes, a Czech artist from 19th century. The lovers take it a bit too far as they are lying on the ground, which would not be considered kosher. It's a hot summer and the sky looks as if there was a storm coming.
French etching called "Le Parapluie Officieux" No 40◊, from the Le Bon Genre series published in the 1820s, show two lovers sheltering under an umbrella in the rain. Through the umbrella you can see a chaperone.
Foxtrot features a strip were Denise is muttering and cursing until it starts to rain, to which she squeals with delight. Peter comments on their newfound closeness; "Wow, good thing you brought this umbrella."
Archie Comics has quite a few examples. It eventually reached the point where Archie and Jughead invented a special umbrella, resembling two standard models attached to the same handle, in case a normal umbrella would prove too small to keep both partners dry.
Three Times: A boy and a girl stand under the same umbrella under the rain, and they tenderly join hands.
Easter Parade has the song "A Fella with an Umbrella," as Johnny falls in love with Hannah while they walk in the rain under the umbrella from a fruit cart, completing the film's Love Dodecahedron.
Anne Shirley is offered shelter under a handsome stranger's umbrella in Anne of the Island, although the romance doesn't last.
A platonic Umbrella of Togetherness (according to most) is conjured by Tris for her and Sandry in the Circle of Magic series.
You can actually hear Captain Wentworth's heart break in Persuasion when he offers to walk Anne home in the rain with his umbrella, and the for-once-oblivious heroine innocently says she already has an escort! What's worse, the ladies in Capain Wentworth's company immediately start gossiping about Anne and Mr Elliot as a soon-to-be-engaged couple.
Agnes Grey: Rosalie Murray thinks she has Mr. Weston wrapped around her finger as securely as every man in town, but Agnes is the one who he walks to the carriage with his umbrella. Awww...
Leave it to Psmith uses an amusing variation as a Meet Cute. Psmith dashes out of the Drones Club with an umbrella for Eve and later refuses to let her return it. It takes her a while to figure out that it wasn't his umbrella to begin with; he stole it for her.
In Daisy Miller, after Winterbourne returns to the Pincio to look for Daisy, the sight of Daisy and Giovanelli cuddling under her parasol makes him turn right around.
Live Action TV
Heroes featured one of Isaac's precognitive paintings (used above) featuring Simone and Peter apparently embracing under an umbrella, which Isaac took to be a sign of their relationship. He's right.
The X-Files frequently made use of this trope. Comically so, on occasion—Mulder (David Duchovny) has quite a bit of height on Scully (Gillian Anderson). Definite Ship Tease.
Used straight-up for courtship in an episode of The Commish. A police officer is advised to take his Girl of the Week to the park. When we see them there it's raining, only it's not a problem as they're both having a picnic under a pair of joined umbrellas.
Buffy the Vampire Slayer. In a platonic love version, Giles walks Willow to the taxi (so she can catch the plane back to the US) under his umbrella.
In How I Met Your Mother, The Mother's yellow umbrella is an arc symbol signifying the love of Ted's life. Narrator — older Ted — made it clear that it had played a major role in their first encouter ("you know the short version [of how I met your mother], the one with the yellow umbrella"), and even before because the umrella had got lost. Ted meets Tracy the Mother at the train station when it's raining. He comes to talk to her and she encourages him to cover under her umbrella with her. It's an example of Meet Cute when they playfully argue over whose umbrella it really is.
In the 2009 BBC miniseries Emma, Mr Weston shares his umbrella with Miss Taylor (future Mrs Weston) when it starts raining after the Sunday mass. In the novel, he met Emma and Miss Taylor when they were walking and he gallantly borrowed two umbrellas for them from Farmer Mitchell's because it was drizzling.
In "Bus Stop" by The Hollies, the main characters continue to share an umbrella even on sunny days, leading others to stare "as if we were both quite insane".
"Bus stop, wet day, she's there I say Please share my umbrella Bus stop, bus go, she stays love grows Under my umbrella"
Rihanna's single "Umbrella" (quoted above) makes obvious use of this image.
"You can stand under my umbrella, my umbrella, -ella, -ella..."
The song "Every Little Thing She Does Is Magic" by The Police plays with this trope; the singer has a crush on a girl he knows, but Cannot Spit It Out. As he says in the song, "It's a big enough umbrella / But its always me that ends up getting wet!" (He gives his umbrella to the girl, instead of sharing it.)
French folk singer Georges Brassens had a song called "Un P'tit Coin d'Parapluie" ("a little piece of umbrella") about a boy who shares his umbrella with a girl, and whose chorus went: "A little piece of umbrella/For a piece of heaven/She sure looked like an angel".
The Hebrew song "Two of Us Together Under One Umbrella" ("Shneinu Yahad Tahat Mitria Ahat") by Naomi Shemer. The refrain, roughly translated:
"Two of us together under one umbrella We're both skipping from one puddle to the next a Raining City has just this to say to us Life's a pretty thing, living life is great!"\\
In The Musical based on Little Women, it doesn't happen quite so as in the book. Bhaer finds Jo at Amy's wedding, on a day riddled with 'sun showers'. He proposes to her with the analogy of sharing a 'small umbrella in the rain'.
Rival Schools: United By Fate features this moment in Kyoko's ending as her to-be fiancee Hideo offers her an umbrella.
In The Legend of Zelda: Skyward Sword, look close at the blackboard in the classroom — there's one of those Japanese umbrella diagrams. While the names are considerably lo-res, and thus almost unreadable, but if you get close to it a dialogue box will pop up with the text "Karane + Caw...".
In Little Busters!, Riki and Kurugaya share an umbrella together while on their first date. At first, both of them try to play it cool and let their own shoulders get wet so the other is fully covered, but they soon realise it's silly and just walk together happily.
The Gaang was given an umbrella from a man that was told by a Fortune Teller that it will rain. Since Sokka is caught up in Arbitrary Skepticism, Katara and Aang are the only ones using it come rainfall.
Zuko and Mai share a huge beach umbrella on the beach — one gets the impression they were going for the "emos hate sunlight" image.
Disney's The Rescuers has a scene where Miss Bianca and Bernard share an umbrella.
Hey Arnold! played this trope as a love as first sight kind of thing between Arnold and Helga as the first time she saw him, and ever felt that anyone ever saw her, was when the rain stopped falling on her and she noticed Arnold holding an umbrella over her head.