In the twenty-third chapter of Asteroid in Love, Ao comes down with a cold, and the Earth Sciences Club visits her. The importance of this episode, however, is why Ao falls sick: her mother discussed with Ao the previous night about Ao's father's upcoming job transfer, Ao fell into a Heroic BSoD and gets sick from sat in the bath for three hours.
A later chapter has Suzu calling in sick from school when overstressed from trying to deal with Shadow Mei. Matsuri stands by her side after class and starts to wonder if he should stop holding their relationship off until his transformation is reversed.
Yomi is bedridden in an episode of Azumanga Daioh due to a fever. She misses out on a trip with the girls to a theme park because of it.
InBakuman。, Mashiro gets hospitalized from overworking himself, resulting in Detective Trap taking a hiatus.
In Ben-To, Sen Yarizui spends episodes 11 and 12 sick.
Ciel is bedridden with asthma and a cold in parts of chapters 28-30.
Ciel is bedridden again in chapters 90-95, this time from a "curse".
In chapter 131.5 Sebastian is ordered to take a rest day and the others treat him like he's sick, having him lay in bed and wear a frilly nightgown.
In the Cardcaptor Sakura episode "Sakura's Dizzy Fever Day", Sakura has a fever but tries to perform her school and Magical Girl duties anyway. She can only do it with Syaoran and Meiling's help (and Syaoraneven gets angry at her because she's not taking care of herself properly, and Meiling has to support Sakura physically so she can seal the Card). Then she totally passes out in bed. Good thing that Nadeshiko's ghost uses her own energy to help her a little.
Heiji's introductory episode happens when Conan/Shinichi has a massive cold. He shows up bringing a special Osakan moonshine as a gift for Kogoro... and tries to feed some to Conan since it's supposed to double as a folklore cure for colds, but he only manages to give him some sips before a horrified Ran interrupts. As the case goes, Conan's symptoms get worse and worse, and he collapses in pain. But it turns out that the chemical reactions within his ill body, caused by the brief alcohol consumption... are actually reversing his forced shrinking, which lets him become Shinichi and best Heiji while resolving the case of the week. Too bad the effects stop right after the case is done, leading to a brief Tear Jerker in which the shrinking Shinichi says he wants to stay older a bit so he can speak to Ran by himself...
More than one episode happens in hospitals as well. So do the arcs involving Eisuke Hondou.
The Whole Episode Flashback regarding a case that Shinichi solved in New York is framed as this: Ran collapses due to a fever after a case, and as she sleeps, she recalls what happened in there...
In episode 1085 of Chibi Maruko-chan, Maruko and Sakiko are worried about their mother when she comes down with a cold. They're forced to do work around the house that would normally be taken care of by their mother as a result. Later, Maruko wonders if she's been overworking her.
Chrono Crusade has an episode where Chrono comes down with a fever after exerting himself too much. Rosette runs all over town trying to find a fever represent that's "strong enough for a demon"—only to push herself so hard that she gets sick in the process. And then it turns out the only cure is for Rosette to kiss him. Which she does.
The Dangers in My Heart: Ichikawa stays home after catching a fever in chapter 37 (Ep. 8), after he forgot his rain coat the chapter before and forced himself to ride his bike through the rain. Yamada visits his house to give him some ice cream from school and he impulsively invites her in for tea. While changing clothes in his room, he succumbs to his fever from exposure and comes close to passing out, leading to Yamada tending him back to bed... Something he later thought was a dream due to his delirium until his sister later gives him a poorly-written "Get well soon!" letter left by Yamada.
In Dear Brother, Rei catches a massive fever when she stays under a heavy and cold rain for hours after Fukiko tricks her into doing so. Nanako finds her and manages to bring her home after much struggle, and discovers her Roomfull Of Crazy. Later, Kaoru drops by and barely manages to keep her in bed so she can give her Intimate Healing via body heat. For worse, Rei is still ill and feverish few later... and it culminates with he trying to go through a Suicide Pact with Nanako, mistaking her for Fukiko.
Happens in Delicious in Dungeon to Marcille. After battling an angry undine, she runs out of mana and becomes very weak. She's bedridden for a while and the rest of Team Touden, plus others, have to find a cure. Their solution is to make the same undine into soup and let her drink it since undine are full of mana.
In Chapter 18/Episode 9 of Denki-gai no Honya-san, Hio-tan takes a day off due to illness, and she's visited by Director, Sensei, and Sommelier for various reasons.
In the original Digimon series, Taichi is temporarily sent back home with Agumon, and they have to take care of his little sister Hikari who is sick in bed while their parents are out visiting their also ill grandma. Later Hikari has a relapse, this time with much more severe symptoms, and as Sora and Biyomon take care of her Taichi, Koushirou and their Digimon have to Find the Cure!. It's made even harder with MugenDramon chasing after them.
Dragon Ball Z: Early during the Android arc, Goku starts feeling the effects of the heart virus that kills him in Future Trunks' timeline. Fortunately, this time around the heroes have medicine to treat Goku with, though he's left bedridden for several days while he recovers, which allows the other heroes to contribute to the plot.
Dragon Ball Super has Goku develop a condition called "Delayed Onset Ki Disorder" in episode 43, which is caused by reckless use of one's ki. In Goku's case, it's because of his combining the Super Saiyan Blue form with the Kaioken.
FAKE has two separate sick chapters, one in which Ryo is sick and Dee takes care of him, and a later one in which the roles are reversed and Ryo takes care of Dee.
In Final Approach when Ryo gets sick this leads to the heroines realizing the girl they really need to compete with is not each other but his sister Akane.
In GA: Geijutsuka Art Design Class, Namiko stays home with a cold, but most of it is about her friends coping with her absence and reacting to her texts.
In Gakuen Babysitters, Ryuuichi falls ill over the summer, leaving him in the care of his adoptive grandmother and his brother Kotarou.
Gintama has a Sick Episode where Tae, Gintoki, Kagura, Kondo, Ayame, and Hasegawa all get sick with the same alien virus, while Shinpachi has to tend to them all. This being Gintama, however, Katsura, of all people, eventually cures the entire gang while serving as a cross between "Ill Smith" and Barack Obama ("Yes, we can!" indeed.). Afterwards, everyone except Shinpachi accidentally turns into "Ill Smiths". To top it all off, the whole sequence was just part of a flashback within the real sick episode. Suffice to say, this series refuses to play its tropes straight.
Chapter 5 of Girl Friends (2006) had Akko being sick with a cold, leading to the first time that Mari hung out with her new circle of friends without Akko present. This led to Mari's realization that their friends considered Mari to be Akko's best friend, even though they've only met this year.
During episode three in Girls Beyond the Wasteland, Uguisu overworks herself drawing art for the game so much that she gets sick. Despite that, she even comes to school, though the others quickly have her rest and recover.
GUN×SWORD has not one but two such episodes, giving each member of the show's central pairing a chance to care for the other. At the end of the first Sick Episode, Van finally learns Wendy's name; in the second one, he opens up and talks about his past. Given that he's The Stoic, it's a pretty significant breakthrough.
An episode of Anime/Hamtaro is about Hamtaro's owner Laura getting sick, so the Ham-Hams try to find a cure for her illness.
In Hetalia: Axis Powers, one story has France teasing a bed-ridden England, only get worried when he realizes that the latter is really ill. America comes by later and tries to cure England by putting a hamburger on his head.
In Hidamari Sketch, Yuno gets a fever and has to stay in her apartment rather than go to school, though she initially thinks she can go despite the thermometer reading. Her well friends who live in the other apartments take care of her when they can, including bringing food and medicine, and, in Miyako's case, changing her pajamas. The anime adds Fever Dream Episode parts as she sleeps off the illness.
In Himouto! Umaru-chan Chapter 22/Episode 10, Umaru catches a minor cold due to sleeping on the floor with the A/C on. The very next day, Taihei catches her cold, and Umaru initially plans to cook some hot and spicy foods as payback for him not staying home to take care of her the previous day. But when she arrives home and sees that his fever has worsened, she's terrified for his health and foregoes her revenge plot to actually nurse him back to health.
Hori catches a summer cold in chapter 20 of Horimiya, spending most of the chapter confined to her bed. That in itself isn't important. What is important is that it leads to Miyamura's Love Confession.
In How to Keep a Mummy, Sora gets sick, leaving Kaede and Mii-kun to take care of him. Due to Mii-kun spending the whole night acting as a cold towel for Sora's forehead, he ends up sick the next day. This leaves Sora terrified of the prospect of Mii-kun dying, until Mii-kun proves he can recover from illness by sleeping underground.
I Can't Believe I Slept with You: Chiyo falls ill, and is unable to make it to a job interview. Landlady spends the chapter taking care of her, and she also deducts a space from Chiyo's debt, partly because she felt sorry for her, and partly because she enjoyed taking care of her.
Used in Inuyasha, when Kagome comes down with a severe cold. The main plot is put on hold while Kagome goes home to rest and the title character mixes up a disgusting "cure."
The finale of season 1 of Is the Order a Rabbit? has Cocoa become sick and nursed by Chino, at the same time Sharo is sick and being nursed by Chiya, then Chino gets sick and is nursed by Cocoa. Truly it is the ultimate Sick Episode.
Junjou Romantica has a chapter in which Nowaki was sick so of course Hiroki freaked out taking care of him. Slight subversion, however, because even though it was invoked for the cliche nursing tropes, the next day Nowaki reveals he wasn't sick at all, just a little tired.
Chapter 79 of Kaguya-sama: Love Is War has Kaguya fall ill and get sent to the hospital suddenly. As she's loaded into the ambulance, it's stated that that she has the capacity for heart disease given her mother suffered from it. During a checkup at her doctor's office, it's revealed that it wasn't even clinical heart problems that caused her to faint in school this time; it was love sickness.
Kirby: Right Back at Ya! has "Something to Sneeze At." Almost everyone in town gets sick, but King Dedede, the Waddle Dees and Kirby don't. Apparently, it's because idiotic people don't get sick. Believing this, Dedede intentionally gets himself sick to prove how smart he really is. Later, however, when he started suffering from the cold, he tried to pass it onto the Waddle Dees and then Kirby, but both attempts failed.
Caterpillar Thriller is a subversion. The beginning has the people in town sneeze constantly and think they are sick, but as Tiff, Tuff and Dr. Yabui point out, they just have a severe case of pollen-induced hay fever. And since the amount of pollen doesn't affect Kirby, Dedede orders the Island Sisters to summon Mosugaba the caterpillar, who soon becomes a cocoon and then a giant moth that spreads its allergy-inducing dust everywhere. It works, but Dedede also gets hay fever since he didn't have it before, either.
In Kitsune no Yomeiri, Ousake spends almost the entirety of Chapter 33 in bead with a bald cold and a fever. A number of his friends come to visit him when they hear about it, bringing their own remedies for him to try. Ousake also suffers from a number of fever dreams throughout the chapter that range from the surreal to a vision of his possible future wife and daughter.
Happens a few times in K-On!—first, Ritsu gets sick after a falling-out with Mio, and then after Mio and the others visit her, Yui catches her cold too, which very nearly ruins their upcoming live performance. The next time, Yui gets sick again, but she gets better quickly and her little sister Ui winds up catching the cold. This helps Yui learn An Aesop about appreciating what you have. When Sawa-chan gets sick, the girls visit her home without actually asking her and everyone but Mugi gets sick afterwards.
Otani gets a fever in a chapter/episode of Lovely★Complex, so Risa shows up to help him out. And then they have an Accidental Kiss, when he passes out on her and their lips meet.
In Lucky Star Kagami gets sick with a cold and is bedridden for an episode. Konata even visits her... to ask for her homework so she can copy it. Later Konata claims to have a spring cold, but Kuroi-sensei doesn't buy it. She's really sick.
In March Comes in Like a Lion, Rei catches the common cold at the wake of the New Year, leading to the Kawamoto sister's bringing him into their home for a couple of days to take care of him.
Michiko & Hatchin: Michiko collapses while driving her scooter, and then tries to shrug off her fever by claiming she just has a very "hot body". Since she's on the run from the law, Hatchin has to enlist a shady back alley doctor/mystic to cure her.
In chapter 42, Tohru nurses Kobayashi who has fallen sick from a cold.
Kanna takes care of Saikawa in a chapter of Kanna's Daily Life. She also attempts (and fails) to invoke a Caretaker Reversal.
In Mobile Suit Gundam, there are a couple of episodes where Bright Noa is laid out in bed sick. Since he was the only senior officer aboard, the helmswoman, Mirai Yashima, takes over as captain, but quickly gets overwhelmed by the job, leading to White Base getting thrashed in a trap.
This trope sees unorthodox usage in Mobile Suit Gundam SEED in an episode where the Le Creuset team is on leave at the PLANTs. While everyone else is going about their business unaware, Rau himself is curled up in his room, laid out with a mystery affliction. He's still expected to work, and no one comes to help him—even if those who cared about him knew, they wouldn't be able to do anything for his sake, after all. Life just sucks like that when you're a clone.
Naruto Shippuden has a filler episode in which Naruto gets a bad cold. Hilarity Ensues. (And Sakura ends up covered in white snot more than once).
Episode 18 of Boruto is about Himawari having a fever. It's used as A Day in the Limelight episode for Himawari and a chance to focus on the relationship between Naruto and his kids. It also reused a short from Boruto: Naruto the Movie about Naruto's inauguration.
In episode 180 of Ojarumaru, Kazuma gets a fever and Ojarumaru decides to go back to his native Heian era to find a medicinal plant that will cure him.
One Piece: An entire ARC arises from Nami getting seriously sick, which leads to the rest of the Straw Hats meeting the reindeer doctor Tony Tony Chopper, who eventually joins them.
Episode 14 of Osomatsu-san had the Sextuplets get sick.
Episode six of Otaku Elf has Elda, the titular elf, coming down with an elf cold, which she caught from fellow elf Yord. Each chapter of the episode focuses on dealing with a different aspect of her illness and recovery, including an Emergency Multifaith Prayer, Elda desperately trying to avoid getting a shot, and having Koito, her Miko, keep her company.
Ouran High School Host Club has a chapter in the manga where Tamaki is in bed with a cold. His fever also leads him to kiss Haruhi's forehead, mimicking what his father Yuzuru had just done. He says it's all right because he's Haruhi's father and drifts off to sleep. After recovering he doesn't remember doing it.
There was an episode where Brock gets sick, leaving Ash and Misty to do the jobs he'd usually do. It's much harder than he makes it look like, and by the end of the episode they've resolved to be more grateful to him. Also crosses over with a Fever Dream Episode as we're treated to scenes of what goes on in Brock's head during his illness.
An Orange Islands episode left Ash and Tracey paralysed by a wild Vileplume's Stun Spore, and Misty had to race to find the Salveyo Weed cure before James and Meowth (Jessie had run into the exact same Vileplume).
Also in the Orange Islands arc, Ash's unruly Charizard came close to death's door after a bout against a powerful Poliwrath, and Ash spent the entire night rubbing his hands raw to ensure that Charizard's flame didn't go out. This fact was not lost on Charizard, and he remains one of Ash's most staunch and powerful allies (at least, whenever he isn't Put on a Bus, anyway).
And a Sinnoh episode had Dawn's Pachirisu come down with a fever, though this was from an electricity buildup (Pikachu had something similar twice before).
Previously, there's another episode where May's Munchlax and James's Chimecho both get sick and have to be taken care of by an old couple whom James lived with as a child. It's more seriousthan usual since James, for all of his Camp and Laughably Evil tendences, actually worries a LOT when Chimecho is sick, and even ends up bonding with May over their common worries. He has to leave Chimecho there, but then a Mime Jr. who's owned by the same old couple gets attached to him and joins him alongside the Terrible Trio.
In another Sinnoh episode, Jessie is too sick to participate in a Pokémon Contest, so James disguises himself as her and competes in her stead. And he even wins.
Kalos has a sick episode where Ash gets a fever from training in the water. When a trainer comes along who wants to battle him, Serena decides to pretend to be Ash in order to get him to go away.
The Pretty Cure franchise in general has quite a few of these with the mascots (Mepple,Milk,Chiffon, and so forth) and some with the Cures.
Suite Pretty Cure ♪, Ellen ends up staying up all night the night before her first day of school, worried/excited over it and she promptly passes out barely into her day. It had two good things to it - it showed that the students there wanted to be friends with her when they saw her pass out and worried for her, and it allowed Hibiki and Kanade to maintain The Masquerade when Ellen earlier began blabbing about her world by saying she was sleep-deprived.
Doki Doki! PreCure had one where Mana overworked herself into a fever on the day of the school festival (however, it looked more like Rikka gave Mana a fever by knocking her over on purpose!). She still wants to attend the festival, but Aguri then tells her the story of The Happy Prince, and tells her she does not want her to suffer his fate.
HappinessCharge Pretty Cure!, Episode 25 has Megumi in bed with a cold and unable to train with the cures, so she is instead tended to by Blue, setting up a love triangle between the two and Hime.
Ranma gets a superpowerful mutation of the common cold after Happosai gives it to him. How powerful? It makes his skin so hot it boils water instantly on contact. Later on, it mutates again so that it flash-freezes any moisture, even from the air around him. At least he (or she, at the time) got to be coddled and babied around by his mother, Nodoka.
There's another episode in which Happosai himself gets badly sick. It turns out that he's dying, and then everyone gets sick when he starts absorbing their Life Energy to hold on to life. Akane is the only one who doesn't fall ill, so she has to find the cure under the guidance of Mio, the local Oracular Urchin.
In yet another episode, Akane catches a cold just as Ranma is accidentally cursed to hug anyone who sneezes. Hilarity Ensues.
For one chapter in the manga, Ukyo is sick in bed with a cold. Ranma, Akane, and Konatsu work in the restaurant, until she's well again. This is also used in the anime, only without Konatsu since he doesn't show up there.
In the second season, the Sailors come down sick except Minako, who attempts to come to their aid as Nurse Venus. Bevery afraidof Nurse Venus.
Subverted in Super S: it looks like Mamoru is coming down with a very serious fever, but it's actually due to the influence of the Black Moon Circus on Earth. He can't join the Senshi in the Grand Finale since he's bed-ridden, and only gets better when Nehelenia is defeated and sealed away.
In Seitokai Yakuindomo, Takatoshi gets sick, and Shino presumes it's because he lent her his umbrella while it was raining, forcing him to go home without one.
In SSSS.DYNɅZENON, Yomogi comes down with a cold and gets bedridden. When the Monster of the Week starts attacking, Chise offers to pilot Dyna Soldier in his place, but is unable to control it due to being her first time, leaving the others with the only option to get Yomogi and have him pilot it.
In an episode of Strawberry Marshmallow, Chika has a cold, and Nobue takes care of her part of the time. When she's gone, Miu pretends to be a doctor. When Nobue returns, Miu has her pretend to be a doctor while the girls who aren't sick take turns at pretending to be patients. Then Miu actually does get sick...
The third episode of the third Tenchi Muyo! OVA series has Sasami falling ill, leading to Noike to take over the duties she did.
A story in the manga had Tenchi falling ill after getting caught between another Ryoko/Ayeka scuffle. The girls get to work in trying to heal Tenchi.
Early in Tenchi Universe, Tenchi grows ill after walking through the snow to get more sake for some of the others. Since everyone is passed out drunk, it falls to Sasami to tend to him, who uses the sapling of Ryu-Oh to heal him, something that Azaka and Kamidake note shouldn't happen.
Tokyo Mew Mew has two, first Ichigo gets a bad cold, later Purin gets a fever from pushing herself far too hard. The girl's only 12, after all.
The episode "Yo-Kai Duchoo" revolves around Nate getting the aforementioned yo-kai to help him play sick so he can stay home and play video games. In the end, he actually ends up sick for real.
In the episode "Yo-Kai Verygoodsir", Whisper catches the "Yo-Kai flu", which prompts Nate to hire a replacement butler until he gets better.
In the episode "Every Cold Has its Thorn(yan)", Jibanyan catches a cold, transforming him into Thornyan.
In the episode "Yo-kai Housekeeper Got It Maid", Whisper catches the "Yo-Kai flu" a second time, which prompts Nate to replace him, this time with a maid.
In Yotsuba&!, Yotsuba gets sick the day her father was supposed to take her to a ranch to learn where milk comes from, leading to a meltdown and day spent in bed. No romantic hijinks, fortunately — just more TV than usual. She finally gets to go a week later.
