Most Slice of Life anime/manga titles follow this trope, such as:
Lucky Star The only character who could even remotely qualify is Akira from "Lucky Channel", and even then she's more of a jerk than a full-on villain, and never actually opposes the main characters.
K-On! is about a group of girls making a Light Music Club in their high school. There's hardly anybody trying to disrupt their dynamics or anything.
Gakuen Babysitters: The story focuses on two brothers (a teenager and a toddler) trying to adjust to a new life after being adopted by an old woman and their parents' deaths. While it's a story that's big on drama from its mere premises, there's nobody working against the brothers, and they have befriended basically every single character introduced.
Azumanga Daioh The closest thing to an "antagonist" is a cat that likes to bite people. Yukari can be a borderline Sadist Teacher sometimes, but even she fails to qualify. Her car, on the other hand, is considered by some to be the true main antagonist, as one ride in it scarred Chiyo for life (though it had more to do with Yukari driving in a way that makes Trevor Phillips look sane).
And just to throw a boys' group in there, You and Me.
Crayon Shin-chan: It's just about a 5-year-old boy who tends to ruin people's lives. It doesn't feature any antagonists unless you count the spin-off, movies, specials, and some episodes that feature them.
Monthly Girls' Nozaki-kun: The only character who's actually mean is Seo, and most of that is just teasing and aggressive basketball playing. The only Hate Sink in the series is Maeno.
Anohana The Flower We Saw That Day: The main obstacle that the still living main characters have to deal with is themselves and how they come to terms with a tragedy from their childhood that they never properly coped with. The characters closest to antagonists in the story are Yukiatsu and Irene Honma, but both are sympathetic characters whose antagonism comes from the way they've mourned Menma's death, and the only real Hate Sink in the whole series is a single Jerkass upperclassman who tries to take advantage of Anaru in episode 5.
Blue Flag: In the end, the story had no single antagonistic force to oppose the protagonists. Most of the conflict is caused by Unrequited Love and the usual challenges of growing up and becoming a young adult. The closest thing the story has to antagonists are Mami (who never really does anything antagonistic outside of being mean to Masumi and Taichi before becoming their friend in the second half of the story) and Kensuke (who fights Touma when he hears that Touma is interested in men and regrets it soon after).
Children Who Chase Lost Voices is an interesting case as there's a lot of danger and quite a bit of fighting but lacks any central antagonist, instead having several brief possible ones, none of which truly qualify. The most noticeable is the Arch Angels who show up in a black helicopter shooting freely, but they quickly escaped and their squad leader immediately surrenders to fulfill his own ambitions. There's the various guardians and Izoka who are more hazards than antagonistic forces. There's the members of the tribe who show up to impede the protagonists but they very quickly leave and go home leaving the climax to be a conflict between two of our heroes which involves body snatching and stabbing, but the instigator of the trouble isn't shown as antagonistic at all and as soon as the conflict is resolved, the one he hurt most hugs him and they all leave together peacefully. The movie easily could have made these threats an antagonistic force but instead, all of its drama is derived from the character's personal problems like a standard No Antagonist work, although it still features a lot of real danger from tangible forces.
In Dragon Pilot: Hisone and Masotan, there is no explicit villain in the story. The focus is on the D-Pilots and their relationships with their dragons and whether they can dedicate themselves to the dragons, even at the expense of other personal relationships. While Iiboshi may seem like the closest to a human antagonist, he only wants the D-Pilots to do their jobs thoroughly and without distraction as the safety of Japan depends on it. Even the giant dragon Mitatsu-sama is not intentionally trying to endanger and destroy nearby lands. It is just that powerful and it requires a human sacrifice to put it to sleep without causing further destruction.
5 Centimeters per Second does not have any character deliberately trying to tear Takaki and Akari apart out of malice.
Haibane Renmei fits this. The most common interpretation is that it's a story about a group of angels in purgatory.
Hitoribocchi no OO Seikatsu is a story about a girl with major social anxiety trying to befriend everyone in her class because her Only Friend broke off their friendship until she could do just that. Bocchi's only real obstacle towards this goal is her own social ineptitude.
Horimiya: The story has no real villain that works against the protagonists, in fact, pretty much every character introduced is eventually added to Hori and Miyamura's extended friend group. This is lampshaded by Sengoku, who, when seeing Sakura breaking down crying after seeing Tooru and Yuki together, points out that one hard thing about this situation is that there is no villain; despite her hurting, no party involved in the conflict did anything wrong or acted with malicious intent.
Isekai Cheat Survival Meshi is all about a modern Earth Ordinary Highschool Student finding himself suddenly reincarnated in an alien world, and the entire conflict involves finding water, shelter, and getting enough to eat each day. The closest thing the story has to an antagonist to date is a dragon coming against Yuu and the two girls, Clara and Katia, who wind up camping with him, and even then, the dragon acts like a mindless beast, simply attacking what it sees as intruders in its territory.
Nightfall Travelers: Leave Only Footprints is about two girls exploring their haunted hometown, and nothing else. There is no antagonistic force, the hauntings are all caused by superstition and scared teens spreading rumours, and neither of the protagonists face any sort of bullying at school.
The Nightmare Before Christmas: Zero's Journey focuses on Zero getting lost in Christmas Town, with Lock, Shock, and Barrel sent to find him. While the trio certainly cause more than their fair share of trouble, they're not malicious about it, and actually legitimately don't understand good and bad. On the elves' side, some of them aren't the nicest characters, but the comic takes place on Christmas Eve, which is the busiest time of the year for them. They're understandably upset that the tricksters' mayhem is getting in the way of preparations.
Subverted in Pokémon: The Power of Us: while Team Rocket is directly responsible for the main conflict by activating balls of poisonous gas, they did it by accident.
Sailor Moon R: In a filler episode notorious for being skipped byDiC Entertainment and uncollected in ADV Films's uncut DVDs, the conflict does not come from any antagonists or monsters, but from Chibiusa's refusal to eat fish, and the protagonists searching for Chibiusa on an uncharted island inhabited by a dinosaur that took her, which turns out to be friendly. The girls do transform into Sailor Senshi to fight off... an erupting volcano.
Shelter is a short film about Rin, a young woman who controls reality with her tablet. Eventually, at the halfway point, flashbacks come into her world she cannot remember, but slowly regains, and we learn why she can do what she does. The film does have conflict in regards to Rin's father, Shigeru, trying to build an escape rocket for his daughter to get free from Earth before a moon-sized body collides with it. Neither Rin nor Shigeru are the bad guys in the story, and the planet is just a giant rock. The conflict rests on an act of cosmic bad luck with Earth just being in the way of this massive celestial body.
Stellvia of the Universe has no antagonists whatsoever, as it is about united humanity trying to prevent a cosmic cataclysm that is about to hit Earth.
A lot of Studio Ghibli/Hayao Miyazaki, especially the Slice of Life, films are like this. Some of them have characters who at first seem to be antagonists but are really not. Miyazaki says that he chooses to not use villains in his children's films because he doesn't really want kids to learn that the world is black and white. In his adult films, the "villains" are usually of the Well-Intentioned Extremist variety for similar reasons.
My Neighbor Totoro: The story centers around the characters' exploration of the rural life they are thrust into and its magical title character. The chief dramatic tension comes when a five-year-old girl goes missing, not from any antagonist.
Kiki's Delivery Service, where the main conflict is Kiki's struggle to forge a satisfying life for herself in the big city.
Ponyo: The main conflict is the massive storm and flood, and while Fujimoto at first appears to be an antagonist, he's really just overprotective towards his daughter Ponyo.
There is no direct antagonist in The Wind Rises. The conflict comes from the inevitable arrival of World War II and Jiro's wife having tuberculosis.
When Marnie Was There is a Coming of Age Story about a girl named Anna, and about the close friendship she builds with the titular Marnie. There is a focus on figuring out just who Marnie is and other events surrounding the film, but there are no real antagonistic characters.
Suzy's Zoo: Daisuki! Witzy completely fits this. There are no conflicts in the world, and the little issues that pop up (forgetting to bring along dessert for the picnic!) are trivial to solve. Then again, this is Kodomomuke fare for infants, so it's probably expected.
Tweeny Witches: The Adventures: The conflict in "The Magical Girls Squad Transformed into Fish!" is about the heads of Arusu, Sheila, and Eva being transformed into fish and their attempt to reverse it. They are trying to keep people from finding and laughing at them, but that's the extent of their antagonism.
Wolf Children: Other than a society that probably wouldn't understand, the only antagonizing force is a mother's struggle to survive while raising two Half-Human HybridWolf Man children.
