A boy wakes up in a strange room and finds a girl passed out with him. They find out they both have weird collars on. The boy has a phone which seems to be connected to the people behind this. They want them to do what?

From MangaHelpers:

There are huge monsters wreaking havoc in Mikagura Kiriwo's city. Building on his father's work, Kiriwo has created a serum that turns him into a giant monster for a short time. He uses this serum to help protect the town from a monster one day--only to find that everyone thinks he's an enemy, too! Everyone at school and in the media hates the "black monster" that he became, due to the massive destruction he did to the town around him. A girl from his class even has to quit school, due to problems caused by the "black monster." Will Kiriwo be able to show that his monster form is really intended to be a savior? [tethysdust]

The "mysterious school comedy" centers on the unusual members of a high-school literary club. Touko Amano, a high-school senior who calls herself the "literary girl" as the club president, is actually a supernatural creature (youkai) that devours stories — she tears pages from books to munch on them. Her club subordinate is Konoha Inoue, a second-year high-school boy who writes stories every day for Amano to eat. He once wrote an award-winning novel, but he wrote it under the penname Miu Inoue so readers thought the author was a mysterious 14-year-old bishoujo novelist. The stress from the novel's fame and its movie and television drama plans turned Inoue into an introverted recluse.

The story centers around the film crew for Idol Survival, the internationally popular television program where swimsuited idols compete in games. The crew arrives on the same isolated South American island that TerraSave member Claire Redfield is visiting on an investigation.

In this world, every child is born under a god. Some gods are weaker than others. Some gods are stronger than others.

Children born under weaker gods become defunct in society, and cannot attend high school. Instead, they must get jobs after middle school. High school in this world is a place that trains students to use their stronger gods. They have one thing in common: They can grant wishes if the correct price is paid.

Leerang turns back time a day, and pays dearly for it. To reverse his wish, he must attend high school and try to use the powers of his cat god once again.

"Hard working" or "passionate" was not in Sakurai's vocabulary and joining a team sports in school was out of the question. But one day, he accidentally walks in on his female classmate Toyoguchi naked in the locker room and in return for keeping it a secret from everyone else, he is forced to become the manager for the female lacrosse team. Toyoguchi is passionate about lacrosse and was responsible for creating the team for the school. Sakurai reluctantly begins his role as manager but is slowly drawn into Toyoguchi's personality and begins researching and enjoying the sport. The once lazy Sakurai who was scared of failure now learns to put himself out there and put serious effort into something worthwhile.

Fushimi is a high-school student who also aspires to be a mangaka. Rin is a model who appears to have some type of psychic powers. What will happen when these two cross paths?

Saitou Shinji is an Ordinary High-School Student living a peaceful life on a peaceful island… way too peaceful for his tastes. The only two things he enjoys on the island are the pranks he plays and the time spent with his Childhood Friend Kana, a cheerful girl who loves taking photos and understands Shinji better than anyone.

However, when he runs away after an incident where he got angry and punched several classmates in the face, he receives a mysterious e-mail on his cellphone: "If you answer this e-mail, you too can become an invisible man!" He answers it while laughing it off… but the day after, everyone has inexplicably forgotten about the incident, and a mysterious white-haired girl appears before Shinji, calling herself an "invisible woman." He soon realizes that answering this e-mail may take away from him the only thing he holds dear…

A manga adaptation of the Chinese literary classic "Romance of the Three Kingdoms".

In the world where the taste and texture of food are very important, there is Toriko, a hunter of precious foods regularly hired by restaurants and the rich.
He's a man with the inhuman skills necessary to capture the ferocious, evasive, and rare animals to complete his ultimate dinner course!
His current accomplice is a weak, timid person who was inspired by Toriko's greatness and accompanies him on all his journeys on his quest for the course of his life.

Note: Was nominated for the 2nd Manga Taisho Award in 2009.

From TokyoPop (based on volume 1):

The World at the Brink of Self-Annihilation

The nuclear age has brought with it the arms race, which has led to the advent of weapons powerful enough to destroy the world itself several times over. Unwilling to take the plunge into Armageddon, the world powers, in league with a group known only as the Black Ghost, have developed super soldiers known as the Cyborgs, designed to fight the wars of the world in space. Unfortunately, the Black Ghost didn't ask the Cyborgs how they felt about their role in the new world order.

This classic work from manga legend Shotaro Ishinomori (Masked Rider) not only told a thrilling tale set against a backdrop of Cold War tensions, but it also helped define the genre of super team stories such as Battle of the Planets, Voltron, and The Power Rangers.

Sakura Kousuke is a boy who strives to throw away a past mired in regret. He transfers to a new school for his second year of high school, believing it will give him a chance to come clean. Ubeknownst to him, however, the appearance of five other "Sakura"s in his class will bring the past to his present, forcing him to come to terms with himself, his old friends, and a girl who, though being Kousuke's complete opposite in terms of personality, also knows him better than anyone else.

Wild's High has a 42-year history as a fighting specialized, girls only, private high school meant solely for the elite. It is also the place that Wild's-League is held: the most popular event in the country and the only place in the world where teenage girls have brutal fights with their lives on the line.

One year the school changed from a girls only school to a mixed gender school. The only male student, Song Jae Gu, has been granted a full 3-year scholarship regardless of grades. Being someone who had to spend every moment either working or taking care of his younger brother and sister, he accepted.

But after meeting Queen, the bloody champion of Wild's-League, drenching her in coffee, calling her a monster, and getting caught seeing her while she was taking a shower... his scholarship could prove fatal.