All humans in this world can use the power of the light of mana, and those who can't are considered to be subhuman 'Norma.' The world is like a peaceful utopia, and the celebrated princess Angelize leads a happy life. She believes that the only darkness left in the world is the existence of the horrible Norma. However, in a ceremony on her 16th birthday, the truth is revealed--Princess Angelize is a Norma. Now she is going to learn what her society does to Norma. She is sent to an isolated island full of others like her, who are taught that the only reason they are allowed to live is in order to fight to protect the peace of this world. Now "Ange" is part of a squad that pilots Paramails and fights invading extradimensional dragons.

Narue is an adorable schoolgirl with a secret. She's really an alien with powers right out of a sci-fi comic! But growing up is never easy, and sometimes it doesn't help when you're from outer space. Join our spunky heroine as she faces androids, alien invasions, and (scariest of all) her very first date!

Note: Won the Seiun Award for Best Comic in 2014.

It's the year 2269, and April Enus is working as a spy for the Alliance. She's known as "Venus" because of her special power: fatalities don't seem to happen when she's around. But is this power a blessing or a curse?

For most people, having one’s own mecha sounds like a dream come true. So when Eiji’s father builds him his own girl mecha to help around the house, he thinks life is about to take a turn down easy street. Unfortunately for Eiji, his eccentric father isn’t about to make it that easy, and his new mecha girl seems to have a mind of her own – one that doesn’t necessarily take to doing what she’s told. Will Akira-chan prove to help Eiji’s life, make it more complicated, or a little bit of both?

Kotarou has an clueless touch--he has an unusual type of ESP that is transmitted via physical contact. When he accidentally awakens his cousin Tatsuki's powers, he comes to realize that there is much more to his powers than he ever imagined!

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!