Kyuutarou Horikita is the tall, dark and handsome... cleaning expert of Kurokado High. His classmates find him mysterious mostly because he's hard to get to know. One day in his club's room in the school's oldest building, he stumbles upon a sleeping maiden: transfer student Fumi Nishioka.

With nowhere else to go and having the eyes to see spiritual dirt, Fumi will learn from the cranky Kyuutaro how to rid the school of the grime that attracts spirit-damaging bugs, and how to fight the bugs themselves.

Has she finally found a place she can call home in the large house of Kyuutaro's small family of sweepers? Will her brazen goal of marrying a rich guy disgust or amuse them? And her heart, once it learns the way of purifying cleansing, will it be cleansed in return—in spite of her missing memories and her ever-looming secret?

Note: This three-volume cleaning fantasy powers up and continues in Queen's Quality!

With SATs approaching closer and closer, can she protect the love and peace in this world? A tale about Han-Yurem, who became a magical girl in her 3rd year of highschool, and the mysteries that surround her.

From MangaHelpers:

28 July 2061 was an unlucky day for Raiji, in which he was falsely accused of being a groper on public transport. That evening, he joined his friends, Yuma and Osamu, to watch Halley's Comet. The comet appeared to arrive a few hours ahead of schedule, but it didn't just pass by in the night sky. Instead, there was a blinding flash, and all the people Raiji and his friends had been watching with vanished. Not only that, but the area around them was suddenly filled with nightmarish giant mushrooms and twisted human faces. In this new, violent world, the three of them will encounter dangers human and inhuman! [tethysdust]

Blue Dragon, Red Phoenix, White Tiger, and Black Tortoise.
To stop the sacred spirits of the Heavenly Realm wreaking havoc in the world of humans, successors of the Four Deities are born in each generation to guard the barrier with the Heavenly Realm, using the powers of the four sacred spirits. And the place they gather to train before they ascend to heaven is Doonggule, a traditional tea house in a small country town.

This manga is set in the Western Xia state at the beginning of the 13th century, when there were violent, ongoing incursions by the Mongol army. Guided by Suzuki, a student who has transferred from another school, a present-day boy called Sudo, a high school student who has been plagued by a vivid dream of a battlefield, is reborn as Shutohel, a female warrior for the Western Xia army, who has lived for vengeance on the Mongols, and travels to the battlefield. At the same time, the Mongol prince Yurul defies his own army, which is trying to destroy the Western Xia script, and makes plans to protect a collection of Western Xia writings. This is an epic, long-form action manga featuring elaborate, dynamic depictions of combat and the enigma of an ancient script.
Note: Won the 16th Tezuka Osamu Cultural Prize's New Artist Prize in 2012.

Takeo, the most unfortunate girl in the universe, pulls on her usual protective gear and goes to her first day at her new school. Having decided to give her parents some relief by living on her own, she ends up, due to a per-usually unfortunate housing mix-up, moving into an inn called Hyakkisou (the Manor of 100 Demons). The life of the young Takeo—or is it Take-woe?—will begin to change the day she sees the youkai... and vice versa.

Affectionately set in an everyday modern Japan with a Hellish war lurking in the background and high-school acceptance issues in the fore, the characters, setting, art and plot all make this story well worth crossing the threshold of Hyakkisou!

From Easy Going Scans:

The Great Shang dynasty has been in power for many years, but the Gods have found fault with the new emperor. Instead of submitting to their will at the expense of his people, the emperor resolves to throw off the Gods' yoke and free humanity. However, this means not only will he face the Gods, but also a rival, the young Zhou—who submits to the Gods' will for nothing but his own purposes!

The fate of the dynasty, nay, the fate of all humanity will be determined by this great battle between the forces of Heaven and Earth!

Sia Lee is a modern vampire that absorbs the energy from touching a human's body instead of drinking the blood. Thankfully, she is a model with gorgeous looks, so she does not have any problems with having relationship with guys. However, Jiho Shin, whom Sia desperately wants to touch, has mysophobia.

After the assassination of the powerful Godfather, Don Pazolini, the world has been thrown into chaos. Many mafia try to fill the power vacuum, but there is a rumor that Don Pazolini's son is hidden away somewhere. That son is Nero, an orphan who is raised in a bar with showgirls as his friends. He dreams of one day finding his parents, but he doesn't know who they are. One day, he encounters a haunted baseball bat, who names himself "Pucchi" and refers to himself as the Pazolini family 'fantasma.' Pucchi insists that Nero come with him to become the new Godfather and rebuild the Pazolini mafia family. Nero is reluctant, but quickly realizes he has no choice, since there is a price on his head and his identity is no longer much of a secret.

Kagefumi Merry takes place before the events of Yumekui Merry, and follows the adventures of a slightly different Merry than we are familiar with.

On the planet Paradyze, a war between the surface and underworld has been going on for centuries. A young cyborg fox named Maze fights for the resistance against the underworld, but has lost hope for an end to the war...until an alien named Grumble crash lands on his planet, and brings with him the technology to change everything...

Plot revolves around high school freshman Shingo Susa as he is invited by his crush from middle school Sayuri Shiroyuki to the school's supernatural club. Over the course of the series Susa begins to gain supernatural powers, something that prodigy Rei Uryu, attempts to awaken to bring out the psychic giant, Susano Oh to destroy humanity and establish a new world order.

Won the 4th Kodansha Manga Award for Shounen in 1980.

From Aerandria Scans:

Noriko is caught up in an accident while she is going to her track and field competition. When she opens her eyes, there is the young doctor Shinoda who seems very concerned about her. She is attracted to his child-like smile, but from his lips, she learns a shocking truth - in the accident, Noriko has lost her physical body and what remains is only a brain, stuck in a little black box?!

Note: The side stories in volume 1, 2 & 3 are written in novel format.

Accompanied by a talking lantern, Mika pursues her sister on a quest to retrieve that which was stolen from her long ago.

Struggling manga author Satoru Fujinuma is beset by his fear to express himself. However, he has a supernatural talent of "noticing things" that forces him to help people.

Boku dake ga Inai Machi Gaiden

A story about a boy who is able to talk to the Gods.

Meedan Kang is the last living descendant of a powerful witch that placed a curse on the Montrose family many years ago. She's desperate to live a normal life but suddenly two handsome men, with ties to the curse, enter her life with different plans for her. Their presence forces Meedan to confront her family's past and the abilities within herself that she has resisted for so long. As the three of them try to face the curse that binds them all together, a love triangle begins to complicate all of their plans.

Beautiful women are being targeted and horrifically killed by an unknown assailant. Cries for justice keep pouring into the police department, but the team assigned to the case is not even close to catching the evasive killer.

Just as they're at their wits' end, a reclusive young man with a mysterious ability arrives and offers the investigators his assistance...

From MangaHelpers:
Yasaka Tokiwa lives in an unusual time, and according to his dreams, it's about to become even stranger. He's been having a dream of a woman called Ri'in ever since the robot, who he calls Makina, came to his home. He and Makina attend the same school, where their other classmates include a secret ninja (Kusanagi Kanata) and a sorcerer (Yata Haruka).
When Tokiwa, the robot, the ninja, and the sorcerer rush to rescue the student council president from a demon, the boys find that they've all been having the same dream! What is going to happen to their world?

Humanity's peaceful days all at once transform into an unspeakably odious hell.
The sudden invasion of wasp-like insects, along with gargantuan "dolls" wielding their enormous alien weapons, annihilating everyone in their path.
In the middle of the chaos, high school first-year, Iruma Ikaruga, fights to save his best friend and his beloved senpai from the dolls' assault with an unyielding spirit.
However, all that awaits him is despair.
Just what are the enormous puppets known as "Dolly"after?
What fate awaits Iruma?
The curtain has risen on humanity's "puppet show" of unimaginable despair, and the battle for survival has begun.