Oyasumi Punpun
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Don't let its initial look fool you. This manga will make you depressed.
Witness the titular Punpun - who is depicted as a tiny, caricatured bird in an otherwise normal human setting - as he copes with his dysfunctional family and friends, his love interest, his oncoming adolescence and his hyperactive mind.
Kansen Rettou
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3 January 2011. ER doctor Matsuoka Tsuyoshi examines a patient presenting influenza symptoms. The next day, the patient dies from multiple-organ failure, followed by others who had shown the same symptoms. As the death toll rises, even the high-tech Japanese are at a loss over how to check the further spread of the deadly virus.
Eden: It's an Endless World!
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In the panic surrounding a worldwide pandemic which kills 15 percent of the population and cripples many more, a secret organization, the Propater, topples the UN and seizes control of much of the world. A boy and a girl, raised in an abandoned virology research center, immune to the virus, use a powerful combat robot to wipe out the Propater forces who come to retake the island, led by the boy's father.
20 years later the boy is the most powerful drug lord in south america. He aids his son from behind the scenes as he evades and eventually with the help of mercenaries from Nomad (some of them former Propater operatives) fights the Propater. Based strongly on Gnostic mythology, all major characters are named after gnostic deities, and have analogous roles.
20th Century Boys (+ the sequel 21th Century Boys)
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Growing older is pretty rough and Kenji is finding out just how hard it can be as life starts wearing down on him. On top of trying to make ends meet running a convenience store, he has to care for the niece that his missing sister left in his care. Memories of youth make it easier, until those memories come back to haunt you.
Kenji and his old friends are slowly being drawn into a mysterious conspiracy that could threaten the world. Who is the mysterious "friend", and how does he tie into Kenji's youth? Why are there disappearances and deaths tied into Ochanomizu University? The friend's memories hold the keys to the puzzle, but years between cloud the clues.
The strange occurrences and the reach of the "friend" conspiracy grow by the day. It will all culminate on New Year's Eve 2000. Will Kenji and the rest of the group be able to put together the puzzle and save the world?
Witches
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A wildly imaginative trek into the deepest realms of human beliefs and the mysteries of the universe. Daisuke Igarashi's amazing pen can recreate anything he can imagine on paper, resulting in beautifully chaotic, maddeningly detailed scrawls of pure wonder. You must read this manga. A true celebration of the human imagination.
Wandering Emanon
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Based on the award-winning novel by Shinji Kajio, Memories of Emanon tells the story of a mysterious girl who holds a 3-billion-year old memory, dating back to the moment life first appeared on Earth. This, Wandering Emanon, is the sequel.
Holyland
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Yuu is a high school kid who doesn't really fit anywhere. To find a place he can belong, be accepted, he will do anything. However one thing leads to another and he is forced to fight to keep his place, his holyland.
Blame!
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In the post-apocalyptic future, the complex networks of machines have created chaos and the human world was destroyed. The robots known as the "Constructer" continued to build a meaningless structure with no one to guide them. Soon these cities reach out to the outer planets and another breed of life form emerges. Follow the journey of a strange man, name Killy, in his search for the understanding of the chaotic world being run by Silicon lifeforms out to destroy him and every living thing in their path.
Sun-Ken Rock
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Ken, a young Japanese guy, is in love with a young Korean girl, Yumin. He followed her in Korea and wants to become a policeman just like her. But then, he finds himself at the head of a local gang.
Gekiryuuchi
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Kei is a high-school student who is bullied on a daily basis...and his classmates, teachers and parents don't seem to care. Pushed to his limits by the endless pain and humiliation, he accepts a strange proposal put to him by his childhood friend Akira; committing suicide together in order to end this nightmare.
The attempt fails -- Kei surviving and Akira disappearing without a trace....
Monster
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MONSTER weaves the riveting story of brilliant Dr. Kenzo Tenma, a famous surgeon with a promising career at a leading hospital. Tenma risks his reputation and promising career to save the life of a critically wounded young boy. Unbeknownst to him, this child is destined for a terrible fate. A string of strange and mysterious murders begin to occur soon afterward, ones that professionally benefit Dr. Tenma, and he emerges as the primary suspect. Conspiracies, serial murders, and a scathing depiction of the underbelly of hospital politics are all masterfully woven together in this compelling manga thriller.
HE∀DS
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The main protagonist, the shy Jun Naruse, is a rather average guy who works for a electronic company and loves to draw. He falls in love with Megumi whom he met at a shop selling drawing materials and an intimate relationship develops. A few days later the office gets attacked and when the criminal tries to shoot a little girl he saves her by jumping in front of her.
A month passes until he wakes up again and is told that half his brain got destroyed and he only survived because someone donated half a brain. Everything seems to be fine, he quickly recovers and is happy, however he begins to change... is the donated brain the reason for that? Or is it just a side effect of the medicine?
Seizon
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Takeda is diagnosed with cancer and feels that he has nothing to live for. His wife also had had cancer, had died of it in fact, and his only daughter has been missing for fourteen years.
One day, when he is about to attempt suicide, the phone rings. It’s the police, and they inform him that the dead body of his long lost daughter has been found, that it appears to have been a homicide....
Kanojo o Mamoru 51 no Houhou
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February 23rd, 20XX.
Looking for a job in the famous TV station at Odaiba, college senior Jin Mishima attended the recruitment orientation. Not far away from the station, Nanako Okano, a gothic lolita trying to attend a concert, found out that her friends tricked her about the concert ticket because of jealousy. The two bumped into each other and "reunited" -- they were junior high classmates -- moments before an earthquake of Richter Scale 8.1 turned the island (the entire city, in fact) into ruins.
Akumetsu
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Nagasawa Shiina is just an average 3rd year high school student until her parents' company goes bankrupt. In order to pay the bills, she sells herself into prostitution. At her first job, a mysterious masked man crashes the party... and it's someone she knows.
Akumetsu is the story of Hazama Shou, who defends his own view of justice in a vigilante manner while wearing a mask and calling himself Akumetsu.
Pluto
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Based off of a story arc from Osamu Tezuka's Tesuwan Atomu, Pluto follows the Europol detective Gesicht as he tries to uncover the mystery behind a string of robot and human deaths. The case becomes much more puzzling when evidence leans toward the murders being the work of a robot, which is something that hasn't happened for 8 years.
Stardust Memories
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Stardust Memories is a short story compilation of human beings in the distant future where we have traveled deep into space. Each story describes a moral dilemma that people traveling in space may experience which is something that we have yet to determine in the current world.
Stardust Memories talk about such problems as the implications of having people travel for years, even decades, in the cold, quiet and endless universe. A different story tells on how human presence in a foreign galaxy will affect the environment. The topics the author decides to write about are interesting and makes you wonder about the future.
Manhole
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What do two Japanese detectives, a naked man on a city street, and a roundworm from Botswana all have in common? In the first volume of Manhole, Ken Mizoguchi and Nao Inoue investigate a string of bloody and mysterious murders, but their work uncovers a deadly biological agent which poses a threat of epidemic proportions.
An unlikely lead starts them in the pursuit of a mysterious self-titled photographer, but meanwhile the infections keep spreading. The series may be best described as the thrilling combination of a detective story with biological horror.
Some might not be exactly what you are looking for, but all of these are high quality manga worth checking out.