From CPM:

An alien armada from Jupiter has amassed enough power to destroy all of Earth's defences. Earth's final hope lies in the Space Battleship Nadesico, a ship created using recently discovered extraterrestrial technology.
Can the Nadesico's rag-tag crew overcome their idiosyncrasies and defeat the alien fleet, or will Earth's last hope be lost?

The manga differs greatly from the anime

[From Viz]:

Ginta Toramizu is a 14-year-old kid who doesn't have a lot going for him: he's near-sighted, doesn't do well in school, sucks at sports, and to top it off--he's short! But Ginta is a dreamer and has had the same dream 102 times, always in the same fantasy world, where he is a hero blessed with all the abilities he lacks in real life.

Then one day a supernatural figure appears at Ginta's school and summons him to a mysterious and exciting new world! In this strange universe filled with magic and wonder, he is strong, tough, agile--and he can see without his glasses! Thus, Ginta begins a mystical quest in search of the magical items known as "ÄRMS," one of which may have the power to send him home. Joining him on this epic journey are his companion Jack and the valuable living, talking, mustachioed iron-ball weapon known as "Babbo," which everyone wants but, it seems, only Ginta can possess!

In a world where demons and humans are at war, there exists a Demon King, whose voice holds a power that destroys all in its way. When an unusual Hero attacks his castle, what's a Demon King to do other than confess his love? But thanks to meddling minions and the inconvenience of a voice that destroys everything in its path, his confession may not go according to plan...

Tezuka teaches about biology in short installments.

Clay, a child prodigy, was hired at the age of 14 to become a professor to make chimeras, creatures made with a fusion of various materials. However, after he was hired, he was unable to meet the expectations of the company that hired him and was fired. He comes upon an abandoned research facility and creates a human child chimera and names him Muddy. Together, they will go out into the world and find out what Muddy is capable of.

From Tokyopop: Nanaki survives a car accident to discover he is psychic. Recruited into an organization that solves cases with psychic powers, Nanaki's average life quickly turns into one of adventure and intrigue. Slacker Nanaki Shunsuke's life is turned upside down when he's hit by a bank robber's car and later meets a strange boy who claims that the accident caused Nanaki to develop psychic powers and that he is required to join LOCK, a paranormal investigations agency or be the suspect of any and every suspicious case that turns up. (thought a summary and categories were need since there weren't any :P If your into Shonen it's a good read :P Sirenic Griffin){Corrections by Silvermagic}

From Broccoli:
When Kaya runs into trouble one day, it’s not a knight in shining armor, but her stuffed animals that come to her rescue. It may sound crazy, but Kaya isn’t pretending: she loves her stuffed animals so much, they come to life and turn into people! Plushies come in all different shapes and sizes, and so do their hearts—whereas some are nice, there are others who are not so kind.

Ash may think he's seen everything when it comes to Pokemon, but is he ready to face the mysterious Darkrai in his latest awesome adventure? While touring Alamos Town, home of the Space-Time Towers, Ash and his friends discover that the town's special garden has been ransacked. Some of the townspeople immediately blame the destruction on Darkrai, a sinister-looking Pokemon said to haunt the garden. But is Darkrai alone responsible for all the strange happenings around town? And what is its true nature? Will Ash and his friends discover the answers in time to save Alamos Town? There is a movie of this.

From the exciting new animated chapter of Ash and Pikachu! Shaymin, the peaceful Gratitude Pokémon, lives happily in forests and fields of flowers. But one day Shaymin is accidentally drawn into a battle between the Legendary Pokémon Giratina and Dialga. Whisked away far from home, Shaymin is found by Ash, Dawn and Brock, who soon discover that this new Pokémon is full of surprises! Of course Team Rocket wants to get their hands on Shaymin, and so does a mysterious man named Zero. Even Giratina is in hot pursuit of this little Pokémon—and just what do Giratina and Shaymin have to do with the dimension known as the Reverse World?

The Continent of Song is in chaos. The sinister secret society known as Demon Card is using the power of Dark Bring to destroy everything in their path.

The only things capable of stopping Dark Bring are the Rave stones. Unfortunately, the Rave Stones were scattered around the globe in an explosion 50 years ago, so now they must be collected by the Rave Master in order to stop Dark Bring once and for all.

This new task has been given to Haru Glory, a sixteen year old boy from Garage Island.

The World's fate now rests on the new, young Rave Master.

From TokyoPop:

After 1000 years of peace, the wolf god Fenris Fenrir has been reborn. She seeks to find the reincarnation of Balder, the most beloved God, as the land of Midgard sinks further into anarchy. They are both key players in the coming of Ragnarok, the time when fate and free-will shall come into conflict as the very nature of the universe is forever redefined.

RilleL:
Based on norse mythology, ragnarök is the term for the end of the world. Christian equivalence would be the last judgement.

The popular Korean MMORPG "Ragnarok Online" was based on this book.

From Tokyopop:
On a world with no women, the surviving men have reintroduced the female in the form of an android. Called Marionettes, they are built to serve men and are limited in their interactions with humans. That is until a poor boy named Otaru Mamiya encounters a Marionette named Lime. Lime is a Saber model with a special circuit that gives her emotions. When Otaru awakens two more Saber Marionettes, his life as an 'average' man quickly becomes as extraordinary as the lives of his eager, busty new friends.

22 years ago a mysterious seismic phenomenon rocked the Yokohama district, thrusting it miles into the sky and effectively separating it from the rest of Japan. In the following years, a fraction of the newborns in this fledgling world began to develop extraordinary powers, each unique to the personality of the possessor. These mutated humans became known as Alters and were responsible for turning the former Yokohama into a chaotic wasteland. Now, as the former metropolis continues to re-build itself, the Alters have fallen into two camps: those who have joined HOLY, a dogmatic organization that hopes to re-establish order and morality, and those who wish to lord over the comparatively weaker humans. Only Kazuma, a powerful Alter who's really only interested in looking out for himself and an orphan girl named Kanami, stands between them, suspicious of both sides and unaware that he may hold the key to harmonious co-existence.

Classic short stories from Takahashi Rumiko. Many are comedies.

Volume 1:
"Fire Tripper" (fantasy, romance)
A gas explosion sends high school girl Suzuko and toddler Shuu 500 years into the past. But she lost Shuu on the way, and as a result, Shuu ended up in the past 10 years before her, and is 15 years old when Suzuko arrives.
"Maris the Chojo" (comedy, sci-fi)
A destructive alien policewoman sees a kidnapped quadrillionaire as her ticket out of debt.
"Those Selfish Aliens" (comedy, fantasy)
Aliens, the government, and fishmen implant bombs in a poor paperboy.
"Time Warp Trouble" (fantasy)
Warriors from feudal Japan inexplicably pop into a high-school classroom.
"The Laughing Target" (drama, romance, supernatural, tragedy)
When they were children, Yuzuru Shiga and his cousin Azusa Shiga were engaged. Azusa aims to make sure that Yuzuru stays hers, no matter what, but Azusa also has a dark secret...

Volume 2:
"Wasted Minds (Dust Spot)" (adventure, comedy, fantasy)
Follows a pair of two bickering government agents, both of whom have special abilities. (A five-part mini-series)
"The Golden Gods of Poverty" (gag comedy)
An unfortunate boy's scientist parents try to use him to make money, but they only succeed in contacting the Seven Lucky Gods, who happen to also be broke.
"The Entrepreneurial Spirit"
A woman leads seminars for a get-rich quick scheme.

Volume 3:
"That Darn Cat" (slice of life)
Takahashi Rumiko remembers having to take care of her neighbor's cat.
"When My Eyes Got Wings"
A couple befriend a sickly child with a secret and his destructive pet bird.
"Wedded Bliss" (comedy, romance)
A wedded couple can only let out their tension from working all day by fighting with one another, until their neighbors threaten to have them moved.
"Sleep and Forget"
A girl relives a past life involving her lover and an evil witch back from the dead in the form of a dog.
"A Cry for Help"
A fairy gives a boy a frightening split personality thanks to the wind-up key she inserts in his neck.
"War Council"
Student councils go to war with one another over a stamp.
"The Face Pack"
A man can change his appearance at will and leads a "masters of disguise" club.

more info here.

The Mana Tree, the giver of mana and life for the world of Fa'Diel, burned down nine centuries ago. A war erupted between faeries, humans, and others seeking the scarce power of mana that was left. When the war concluded, the drained Mana Tree slept and throughout the many lands of the world mana was stored in ancient artifacts.

Toto, and his pet Rabbi, have set out on an adventure to restore the world, and its mana, to its former self.

The Lands of Fa'Diel are populated with a large number of different creatures, including humans, faeries, demons, the jewel-hearted Jumi race, plant-like Sproutlings and Flowerlings, miner bears called Dudbears, and shadowy beings of the Underworld known as Shadoles. Fa'Diel is also the home of a host of anthropomorphic animals and objects, as well as monsters such as Rabites, Chobin Hoods, and Goblins.

Adaption of the PlayStation game of the same name.

From Tokyopop:

Fifteen years ago, a set of twins--a girl and a boy--was born to the king of Linevan. Shortly after their birth, a prophecy foretold that when the girl turned 16, she would bring about the end of humanity. To avoid this terrible fate, the king ordered the princess disposed of...scrapped!
She miraculously survived and was raised away from the kingdom that would kill her. But now she has turned 15, and the king's guards have caught wind that she's still alive...and they set out to finish the job!

From Turtle Paradise: After being shipwrecked on a remote southern island, Lina and Co. protect its townspeople from an attack by pirates…. But the island holds a deep, dark secret - and powerful magical forces are at work trying desperately to hide its past. The fate of the world once again rests in the hands of the over-bearing Lina Inverse… For better or worse! Join Lina, Gourry Gabriev, Zelgadiss Greywords, Amelia Wil Tesla Seyruun, and introducing Luke and Millena on a brand new adventure!

From Manga Art:
After Daa! Daa! Daa!, Ruu is now a cheerful youth living in his home, Planet Otto. Then, a confused girl named Miu arrives through a wormhole from Earth. Ruu joins up with her and promises to take her home. Unknown to Ruu, Miu is the daughter of the same people who took good care of him in his stay on Earth.

After meeting the enigmatic woman Hureika in a sideside village during her travels, the beautiful genius sorceress Lina Inverse’s fate takes a dramatic turn. Separated from her partner Gourry, she finds herself swept ashore onto an unfamiliar land. Faced with violent monsters, she is suddenly unable to wield her magic…. But her grand adventures only begin once she is saved by Lyos, a boy who claims himself to be the “Knight of the Aqua Lord”….

Alternate retelling of the Slayers TRY anime.