Rain Jewlitt, known as the Methuselah, is a spaced-out, immortal, 624-year-old man dressed in priest's clothes. He's got eternal youth and a large price on his head—put there by those questing after the secret of his immortality.

Machika Balfaltin is a tomboyish, energetic 14-year-old girl who, upon the death of her grandfather, sets out to kill Methuselah, the one bounty her assassin grandfather, Zol the Grim Reaper, couldn't kill. Instead, however, Machika ends up being saved by Rain again and again from other aspiring bounty hunters attacking them both.

Sound like the beginnings of an odd relationship? You won't believe where their journey takes them...

From Infinity Studios:
With the invention of the automatic vacuum robot and the time-set video recording devices, what is the next breakthrough in home appliances? Why that would be cute female mini-robots that kill bugs of course! In Ichigeki Sacchu!! HoiHoi-san, a corporation in this alternate universe has created such a pest control agent and it’s the hottest selling item ever. Journey along with one enthusiast of these robots called HoiHoi-san’s and experience the joys & suffering of being a dutiful owner of these new adorable, bug killing, wallet busting machines.

A slacker high-school student gets pulled into a world where he is named the "Dungeon Master" and can control everything that happens. He can even make it rain money! It's in this world that he meets a young, traumatized girl who's memories have been erased. With her help, he creates a new game world to escape his boring school life. Everything seems to be going fine until they encounter a lethal bug in the game's programming.

From Seven Seas:

Being a girl is harder than it looks...
For Hazumu, this couldn't be more true, because just the other day, she...was a he.

Shunned by the girl of his dreams, Hazumu loses himself in the mountains and is promptly squashed by an oncoming space ship. The alien inside, feeling guilty, rebuilds Hazumu's body...but as the wrong gender!

Now Hazumu must learn how to be the girl his parents always wanted while dealing with the trials and tribulations of being caught in a love triangle between two girls--his childhood friend, Tomari, and Yasuna, the girl who rejected him but is now strangely attracted to him/her!

Maico is a charming young woman who also happens to be an android. Her creator built her to revitalize the flagging ratings for her radio station, as well as to probe the intricacies and weaknesses of the male libido. Maico quickly becomes entangled in a very human love triangle, not to mention the scandal and intrigue surrounding the station, its competitors, and the hordes of adoring fans that this sexy new personality attracts.

Mazinger Angels chronicles the adventures of four women who pilot giant robots in the Mazinger vein. The concept is a spoof on the late 70's and early 80's popular TV series Charlie's Angels.

Three of the robots, Aphrodite A, Diana A and Minerva X are from the original Mazinger Z series, while Venus A is from the Great Mazinger series. Their pilots are also traditional characters from Go Nagai's universe, Sayaka Yumi and Jun Hono from Mazinger Z and Great Mazinger respectively, and Hikaru Makiba and Maria Fleed from Grendizer.

The style of the manga highlights the sex appeal of both the characters and the mechas, sometimes similarly to the way Aika's female characters are shown. (taken from wikipedia)

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

Tezuka teaches about biology in short installments.

From Aku-Tenshi :

Because her father was sent to London to work, Natsumi, a 4th grade student, also must leave Japan along with him. Her classmates throw a farewell party for her. Natsumi is prepared to go to London, but on the night before Natsumi's arranged departure, a baby suddenly appears in her house after a roar of thunder! What's more is that this little baby is actually the one that Natsumi will give birth to in fifteen years!

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 ADV: Imagine a Neon Genesis Evangelion where choosing the right girl is more important than saving the world! That's the gist of Angelic Days--the hit manga that Eva fans have been waiting for! Based on a popular PC and Playstation 2 game released only in Japan, Angelic Days takes the angst-ridden Eva pilots and sets them in a lighter, brighter world.

Rocket Princess was written by Nobuyuki Anzai before he started his work on Flame of Recca.

Basically, we follow Ishibashi Kango through his days as he interacts with a cyborg by the name of Oozora Kohime.

If you liked Flame of Recca, then I'm pretty sure you'll find something to like in this one, too.

Tsutsumu Shisui is brought up by his grandfather, Dr. Yuujirou after his father, Dr. Hiromu died. But now Yuujirou also died with a lot of debt. At Yuujirou's funeral, Tsutsumu's cousin, Sou Takigawa suddenly appears and declares that he wants to take care of Tsutsumu.

[From AnimeWaves]:

Chinami was born with psychic powers. She has always wanted to join the Psycho Police Force. However, she doesn't know how to control her powers, so she failed the entry exam. However, after being saved from a psychic criminal, she joins the Psycho Merchants instead.

[From Aku-Tenshi]:

In the center on a metropolis city lies a small, shaky-looking house. A normal... Okay... Not so normal high school student, Sakura Tetsu (and his family), who works day and night relentlessly to support his family's living expenses, lives there. All is normal until one day, people from the future, alien pirates from outer space, appear. The underground kingdom claims Tetsu's land. Will he prevail in protecting his own land? Or will he surrender his land into many more invaders to come? Yes... Weirdness and insanity ensues!

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.

1-2) Sensei to Himitsu
Kaji's woken up from his nap hearing popular Tsunoda-sensei getting hot and heavy with another guy! But it's his partner, the plain Aritou-sensei that Kaji can't stop thinking about. Kaji's eyes are being opened as he finds that the needs and dark desires that can bind together lovers aren't always about love...

3-6) Hold me for all of Time
A researcher, Sawatari Kaoru, runs off after finding out that there will be no more funding for his research. As he wanders around he sees an abandoned warehouse where he could use to continue his research with his remaining savings. As he walks inside the building, he meets an arrogant little boy. Surprise ensues as to the boys identity, and the unexpected result of his own research...

Extra) And then...
Continuation of ch.1-2, a little into their future.

On the once-peaceful planet of Industria, constant battles have been fought over control of the planet. Astro is a dim witted but kind boy who tirelessly works to feed his "family," a group of orphaned children. One day, after being fired from his most recent job, the prince of Industria, Bulge, appears in front of him. And even more shocking, Prince Bulge looks and sounds exactly like Astro! One thing leads to another, and Astro now has to take Bulge's place as the heir to the throne of Industria! Suddenly, he's faced with the task of bringing peace and harmony back to this war-torn planet!

- Red Hawk NEO