In the manga, of course, this is out of necessity — there are still two beds, but the room is shared with Yuuichi, who naturally gets his own bed. (Although it's implied that they previously slept in the same bed anyway.)
Miyuki and Natsumi of You're Under Arrest! fall asleep together in their patrol car at the end of OVA episode 2, "Tokyo Typhoon Rally". By the end of the OVA series, they've moved in together — to save on expenses and travel time. Poor "Kenny" Nakajima might die of hemorrhagic shock before his nose quits bleeding. Afterward too, since all the official art is a complete and utter explosion of Les Yay...
Kou and Aoba in Cross Game, all the sweeter since if Aoba had woken up first, Kou would have been a dead man.
Noir took this to then-new heights, including several classic There Is Only One Bed scenes, all of which were played completely straight (and quite sweetly).
In the novels, Mikuru Asahina and Haruhi are seen sleeping peacefully like that. But it does give a good impression of their friendship, given to that poor Mikuru usually is nothing more than an abuse doll for Haruhi. Kyon also comments on it, and also says that they could "rival each other [in looks] right now". Then he later remarks that that's because her mouth was shut, and she wasn't being her bossy self. To all the Kyon/Haruhi shippers, Kyon's lying to himself. To everybody else, he's still free for her/him/it.
It also happens in the second season of the anime in the second part of "Endless Eight".
Happens to Wolfwood and Milly in Trigun. (From Wolfwood to Milly: "You're comfortable.") This makes Meryl and Vash have to sit next to one another as they express annoyance at their companions' behavior.
Non-shipping example in episode 8 of Utawarerumono, with Aruruu, Yuzuha, and Kamyu sleeping on top of Mukkuru.
In Twin Spica this happens between Asumi and Marika during the grueling closed-environment test, which might have been the trigger for Marika's defrosting process.
Lithuania, exhausted from being overworked by his boss Russia, unintentionally falls asleep on a couch only to wake up to find himself beside Russia, who for once is in a genuinely good mood and gently asks him about what he's been dreaming of.
Subverted with Greece and Japan. It looks like Greece is gonna pull his on Japan... but after dozing off a little, he wakes up and acts like nothing happened.
An episode of Slam Dunk had the main five falling asleep in a heap in the locker room after a particularly tiring game. Yes, the Ho Yay fangirl squees could be heard across the globe.
The Beach Episode of Yotsuba&! ends with a panel showing the entire group slumped into each other, asleep, on the train back home. There's an extra "The End" panel showing that Koiwai has slid onto the floor...
Subverted in the AKIRA manga. Yes, Kaori looks sweet and peaceful when she sleeps with her head on Tetsuo's lap, but then we see that Tetsuo is in extreme pain and his arm is mutating again.
Happens in the manga and anime of Spiral with hero Ayumu and sidekick Hiyono; the thing is, he's very aloof and she's the stereotypical annoyingly cheery air-head, but they've just saved each other's lives and he hasn't slept much in two days, so he asks to sleep on her shoulder. While calling her annoying. Probably the cutest moment of the entire anime, though the manga topped it when it started fixing romantic entanglements.
Rose of Versailles: The manga features a scene where André is reading the newspaper while seated next to Oscar. Oscar falls asleep on his lap due to sheer exhaustion. André is delighted to say the least. They had not become a couple yet.
In episode 124 of Ranma ˝, Sentarô and Satsuki meet and it's love at first sight. They stare at each other for so long that Ranma and Akane, waiting for them to actually say something, fall asleep, resting against each other until the next morning.
In a non-romantic example, Spider-Man and Spider-Girl get a father-daughter version of this. It's even sweeter in context, having come after an issue where they spent most of their time bickering at each other before reuniting an Ex-Villain and his daughter.
In one fairly recent Superman comic, Supes and Wonder Woman do this after a difficult battle, prompting Lois Lane to observe the two of them and make an aside to the audience that it's a good thing that she's not a jealous woman. (This is used mostly to note Lois' character development, because she was jealous of Supes' and Diana's relationship not that long before this story.)
In a scene towards the end of Scott Pilgrim Gets It Together, Scott, Stephen, and Joseph are recording a song, while in the background, Kim and Ramona are shown to have fallen asleep (presumably from boredom), with Kim's head on Ramona's shoulder.
The Question: A platonic version occurs between Vic Sage and Renee Montoya when they fall asleep on a long plane ride and Vic slumps onto Renee's shoulder. It's kind of cute considering how much time they spend bickering and snarking at each other when awake.
This happens, of all places, in a Sin City story. Miho, the resident Dark Action Girl, falls asleep on the lap of Dwight McCarthy in the story Family Values. This is sandwiched between scenes in which Miho carves up an entire mob family.
Parodied in a 1989 Fox Trot strip (and an obvious non-shipping example, since they're brother and sister). During a long plane trip, Paige falls asleep on Jason's head. Luckily, this quickly stirs the both of them awake and causes them to scream in terror.
Destiny's Pawn has it in the Kashyyyk chapter. The entire party is holed up in Jolee's cabin for the night. Bastila notices the sleeping arrangements of Kairi (Revan), Mission, and Carth with dismay.
Bastila struggled for sleep, but found it would not come. Across the fire pit, she saw Kairi sleeping between Mission and Carth. The Twi'lek girl and Kairi were face-to-face, Mission's blue hand clasping Kairi's. Poor girl. Bastila knew she was deeply hurt by the loss of her constant companion, and there was little doubt that being alone and asleep in Taris's Lower City was a gamble at best. As for Carth, he had fallen asleep on his stomach, one arm flung around Kairi's shoulders. With a muffled grumble, he shifted to his side and used one arm as a pillow. He wasn't spooning with Kairi... yet... but his hand sleepily groped around until he found Kairi's and Mission's, and topped their hands with his. As much as he claimed he trusted no one during the day, he could hold no secrets in sleep. He already had bonded to them, perhaps irrecoverably. What else could go wrong with this assignment?
Subverted in Total Drama Battlegrounds when Joel and Daisy cuddle together in their sleep. The others tease them in the morning about it, while they say it has nothing to do with romance. Sure enough, they both wind up paired with other people.
Shinji and Asuka at the end of EvangelionRE-TAKE. It's a very minimalistic example, since their fingers are only barely touching the other's, but for them, it's an extremely meaningful show of affection.
In Final Fantasy VII: Advent Children, Cloud and Tifa sleep curled together in a bed of flowers in Aerith's church. Of course, this is because Tifa has been knocked unconscious by Loz and Cloud has terminal geostigma, but it's still sweet to the point of hyperglycemia.
Zig-zag: In Wreck It Ralph, Vanellope shows Ralph her hideout within Diet Cola Mountain in the "Sugar Rush" game and how she tucks herself into bed using candy wrappers as her blankets.
Films — Live-Action
In the Lizzie McGuiremovie, Lizzie and Gordo fall asleep this way on the way to Rome early on. Gordo eventually awoke and realized the situation, but decided he didn't mind, and went back to sleep.
Early in It Happened One Night, Ellie sleeps on Peter's shoulder during a bus trip. Later, he says to her: "Remember me? I'm the fellow you slept on last night."
Ron and Hermione are sleeping next to each other, with their hands lying so they appear to be reaching out for each other.
Tonks and Lupin are posed like this as they're lying dead in what's left of the hospital wing.
Cop 633 and Faye have one of these one fine afternoon at the former's apartment in Chungking Express.
Happens twice in Leap Year. First when Anna spends the night on a bench with Declan as they wait for the bus (him sitting upright, she with her head in his lap and his coat serving as the Comforting Comforter). When they finally catch said bus, it happens yet again with her head resting on his shoulder.
Used in This Gun For Hire, gaining plot-relevance when the sleepers are seen and mistakenly linked together by a third character.
In The Karate Kid (2010), Dre falls asleep and leans sideways onto Mr Han's lap who hesitantly places a hand on his back. His hesitation makes more sense when you realize his deceased son would have been the same age as Dre.
Ron and Hermione in Deathly Hallows definitely qualify: the first night they spent in Grimmauld Place, they fell asleep holding hands. Harry even remarked how seeing them like this "made him feel strangely lonely".
And so Gollum found them hours later, when he returned, crawling and creeping down the path out of the gloom ahead. Sam sat propped against the stone, his head dropping sideways and his breathing heavy. In his lap lay Frodo's head, drowned deep in sleep; upon his white forehead lay one of Sam's brown hands, and the other lay softly upon his master's breast. Peace was in both their faces.
Subverted slightly in Nation: Daphne has to sleep next to Mau in a rather cute moment. However, she quickly discovers that having a person asleep on your arm is a good way to get pins and needles.
Wicked has scene where Glinda and Elphaba sleep together. To quote it:
In a single lumpy bed, they huddled together for warmth and encouragement and, Glinda told herself, protection... Glinda would start as if from a frightful dream, and nestle in nearer to Elphaba, who seemed at night never to sleep.
There are several particularly cute ones in Moby-Dick of all things, involving Ishmael and Queequeg, one of which is quoted here:
We had lain thus in bed, chatting and napping at short intervals, and Queequeg now and then affectionately throwing his brown tattooed legs over mine, and then drawing them back...
Katniss and Peeta are all over this trope in The Hunger Games. Katniss intentionally invokes it since it's a convenient way for her to make people believe she's in love with him.
Percy and Annabeth in The Heroes of Olympus. They get up at night to go cuddle in the stables, and end up falling asleep together. Then Frank finds them in the morning. Annabeth ends up getting grounded.
In the American version of The Office, Pam falls asleep in this exact pose on Jim's shoulder during one of the interminable conference room meetings. Even though he's had a rotten morning and lost his main sale of the year, this little gesture from Pam is enough to let him decide that he's had a pretty good day.
Happened entirely by accident in private to Ross and Joey in Friends. After concluding that it was the best nap both had ever had, and that it didn't mean anything, they voluntarily do it again... and woke up after the rest of the group had been staring at them for several minutes.
In the Mork And Mindy episode "Sky Flakes Keep Falling On My Head", Mork and Mindy fall asleep huddled together in Exidor's literally falling-apart summer home to keep warm from the snow. Unfortunately, because they fell asleep, their fire went out...
The Middleman has something similar between the Middleman and Wendy, only they were both awake, albeit extremely bored.
In an episode of Scrubs, Doctor Cox awakes in the break room to find that his arch rival Doctor Kelso is sleeping with his head in Cox's lap. His response is a resigned "fair enough".
Tony and Ziva end up like this in the NCIS season 3 episode "Untouchable". The "cute" factor is somewhat mitigated by Ziva's loud snoring... still cute◊.
In the "i Dream of Dance" episode, Freddy, Sam and Carly fall asleep on the couch together. Interestingly it's Sam and Carly who lean against each other. You may draw your own conclusions.
Same episode, after Sam's dream sequence, Freddie has his own dream sequence (where he defends Carly's honour in a dance fight), once it's over, there is a textbook Sleep Cute shot with Freddie asleep but smiling, and Carly asleep and resting on his shoulder.
Gossip Girl's Chuck and Blair waking up in the back of his limo, holding hands.
Vampire Diaries' Stefan and Elena waking up in bed together in Season 2 Episode 6 "Plan B".
At the beginning of the Skins episode "Maxxie and Anwar", the class travelling to Russia on a plane — Maxxie is sleeping with his head resting on Anwar's shoulder. Maxxie wakes up and notices that Anwar has an erection, which Anwar insists is due to the plane's vibrations.
Dollhouse: At the end of an episode that showed all the horrific thingsSierra went through before coming to the Dollhouse and the fallout of those events, the closing shot is of her and Victor, cuddled up in the same sleeping pod.
In an early episode of The O.C., Ryan, Seth, Summer and Marissa are forced to spend the night in a hotel. Summer and Seth have the bed while Ryan and Marissa share the pull out couch. Ryan and Marissa wake up spooning, and we cut to Summer telling Seth she didn't want to wake them up because they looked so cute together.
Firefly episode "Jaynestown". After a night drinking Mudder's Milk and singing "The Man They Call Jayne," Kaylee and Simon end up sleeping in the bar, on a bench, Kaylee on top of Simon. Simon being Simon, he manages to ruin it as soon as they're woken by The Captain. Here's a picture. Aww.
Castle: Episode "Close Encounters of the Murderous Kind" Rick Castle and Detective Beckett wake up in her police car after they were taken, interrogated then drugged by mysterious government agents. Later they are asked "Are those hickeys?" "They're from the injectors" he answers.
In "Amy's Choice", the Doctor, Amy, and Rory fall asleep against each other a few times. The most adorable is probably on the bench in Upper Leadworth: the Doctor and Rory fall asleep touching foreheads.
Keen Eddie: Eddie and Monty in The Amazing Larry Dunn wake up like this in Monty's car after a stake-out.
Ashes to Ashes: Subverted by Gene and Alex falling asleep in Gene's office after bugging Mack's office... and Alex is snoring.
In one episode of Boy Meets World, Cory and Topanga are working late on a project at school and they happen to fall asleep next to each. However, when other students see them the next morning they think they had sex.
Mike and Amanda in the Supah Ninjas episode "Detention". Turns out she's a drooler.
Invoked in The City Hunter when Yun Sung falls asleep on Na Na's shoulder. She tries to surreptitiously push him away, gives up when he doesn't budge...and fails to notice that he's grinning.
An early episode of Moonlighting has Maddie sleeping on David's shoulder on an airplane. Memorable for David's line: "Don't pretend you're not impressed. We're sleeping together."
The Everly Brothers song "Wake Up Little Susie".
The album art of "Brain Thrust Mastery" from We Are Scientists.
As evidenced by the page quote, Vienna Teng's Recessional.
Engelbert Humperdinck's opera Hänsel und Gretel has this when the children go to sleep in the woods for the night.
It is possible to invoke one of these in Persona 4. When Rise (who, along with Yukiko, may or may not be drunk at the time) drags everyone into a party game. Choosing the right option will result in Rise sleeping with her head in the main characters lap.
At the end of Persona 3, the protagonist falls asleep with his or her head in Aigis's lap (or alternatively, in a New Game+ , that of his or her chosen love interest). Unfortunately, he/she never wakes up, thanks to previously sacrificing his/her life force to prevent the End of the World as We Know It.
The end of Shadow Hearts with Yuri and Alice. It's cute in the happy ending; they wake up and smile at each other. In the canon ending, he wakes up and realizes she's dead.
In Yakuza, 9-year-old Haruka falls asleep with her head in Kazuma's lap while riding in the back seat of a car. That in itself is cute enough, but in Yakuza 2, there is a similar scene where Kazuma falls asleep with his head in Haruka's lap.
The save method in ICOis sleeping cute. Extra points to the programmers for adding a little animation of Ico carefully sitting up with his head turned so as not to hit Yorda with his horns, when they wake up after their game-saving nap. You can even press R1 (the "call Yorda/hold hands" button) to turn Ico's head toward Yorda's while on the couch, who will respond in kind.
In the Opening cinematic of Kingdom Hearts II, Sora is sleeping on the beach, holding hands with both Riku and Kairi. Serves as ship tease for both straight and yaoi pairings.
After completing Mass Effect 2, if you romanced any of the characters, there's an option to sleep in together in bed, cuddling and resting. Awww.
Lynch and his fiancée Xiu at the start of Kane & Lynch 2: Dog Days. This serves to make it more poignant when she's killed by Hsing.
Final Fantasy VII: Crisis Core: At the inn in Nibelheim, right before the big event and Sephiroth's big Face Heel Turn, Cloud and Zack stay up late talking and then fall asleep in adjacent beds. Shippers, start your engines.
inFAMOUS 2 gives us Cole and Zeke in a total Bromance moment. Cole is about to absorb the penultimate Blast Core, but he and Zeke decide to just relax for once and watch TV and drink beer, ignoring their phones/radios. Fade to several hours later and the two are leaning on each other.
Clannad: In the Visual Novel (unlike the anime example above), Fuuko and Tomoya. And then Tomoya wakes up alone. The nicest bit is when Tomoya's made to remember Fuuko afterward, and finds she's been invisibly following him around since then.
In Lilly's route, Hanako falls asleep on Lilly's shoulder as the two and Hisao take a train tide back to Yamaku from Hokaido. Lilly lets her nap as she and Hisao make small talk.
Little Busters: The last CG in Mio's route is of her falling asleep on Riki's shoulder as they sit together at lunch under the zelkova tree.
a2 ~a due~: After Hao and Sona stay up late into the night arguing over orchestral decisions, they fall asleep next to each other on the floor. Next morning, their orchestra members find them and start taking pictures with a cell phone, even more convinced now that the two of them are absolutely smitten with each other.
Cello player: Hey, give that back! No, don't delete it! It's too cute to delete!
Trumpet player: Yeah, we can Photoshop out your drool!
Sona: Do you honestly think that's the real problem here?!
The Christmas Episode "Comfort and Joy" ends with Hawkgirl and Green Lantern resting against the counter of a bar. Hawkgirl gives the unconscious Green Lantern a peck on the cheek before she lays her head on his shoulder and goes to sleep.
To slightly subvert this trope, John is also pressed up against a giant grey-skinned alien that they had been fighting earlier in the Bar Brawl.
Happened between Fry and Bender once on Futurama, when they got bored watching TV. They promptly fall asleep in the very same position once they become bored with what Leela wanted to watch — which being Futurama, takes all of four seconds. They scramble apart when woken up but not much is made of it.
While on a long car trip in one episode of ˇMucha Lucha!, Buena Girl fell asleep on Rikochet's shoulder.
Danny Phantom: Danny and Tucker accidentally sleeping together is the most hilarious non-gay moment ever.
Happens with Ashoka and Bariss in the Star Wars: The Clone Wars episode "Brain Invaders". Granted, they were practically freezing to death since life support had been sabotaged and Bariss had just been freed from a mind-controlling worm. Here.◊
Martin and Chris invoke this trope accidentally. In "Voyage of the Butterflier XT", they're tired after their long journey to Mexico, and decide to hibernate with the butterflies. Eventually, cut to scene of Martin sleeping on Chris... and using his ass for a pillow.
Again in Elephant in the Room, except the elephant calf put Chris on top of Martin after stealing their blankets. Didn't stop them from falling asleep, though...
In the The Legend of Korra episode "The Revelation", Mako and Korra fall asleep this way while staking out Republic City Park, and wake up with hasty awkwardness when they realize the position they're in.
In the Futurama episode "Neutopia", everyone gets their gender-defining characteristics removed and as a result, everyone starts to get along better. This includes a rather heartwarming scene of Leela and Amy sleeping next to Fry.
Mated pairs of otters do this on purpose. Because they sleep floating on their backs in the water, they'll anchor themselves to any convenient seaweed with one front paw and hook the other around their mate's so they won't drift apart while they're sleeping.
Many, many small mammals sleep together in a pile, both to share body heat and to fit as many as possible into a burrow or nest without having to make it bigger.
In Real Life close friends may sometimes use each others shoulders as a pillow. Don't assume they're a couple though; it might turn out that they actually areJust Friends and would find it a bit weird to think otherwise. However, couples also do this.