A Certain Magical Index

Set in a city of scientifically advanced superhuman students, but in a world where magic is also real. Touma Kamijou’s right hand, the Imagine Breaker, will negate all magic, psychic, or divine powers, but not his own bad luck. One day he finds a young girl hanging on his balcony railing. She turns out to be a nun from the Church of England, and her mind has been implanted with the Index-Librorum-Prohibitorum - all the magical texts the Church has removed from circulation.

A Certain Scientific Railgun

Academy City is a highly developed place in terms of technology. It is said to be 20 to 30 years ahead of the rest of the world, and 80% of its 2.3 million residents are students. The focus of studies here is directed towards esper powers. Misaka Mikoto, one of the top level espers in town, shares a room with Kuroko Shirai, another high level esper who is a member of Judgement, a law enforcing agency composed of students. Both attend Tokiwadai, a private school reserved for the high-leveled and the rich. Kuroko's partner at Judgement, Kazari Uiharu, is a low level esper who studies at Sakugawa middle school. Her best friend and classmate there is Ruiko Saten, a level zero, one who has no esper powers. Together, the four encounter several adventures in the exciting scientific town. (Source: Anime News Network)

Gate

The military fantasy series begins when a gate appears in Tokyo's Ginza district sometime in the 21st century. From the gate pours out monsters, knights from middle-age Europe, and other fantasy-like beings, and they kill many of the citizens of Tokyo. This event is known as the Ginza Incident. The government sends a small group of soldiers from the Japanese Self-Defense Forces (a replacement for Japan's military) to the alternate world beyond the gate. Led by otaku soldier Youji, they find that the villages in the world are being attacked by a dragon. An elf girl who is a survivor from the dragon's rampage joins the group in their travels across the dangerous new world. (Source: Anime News Network)

A Certain Scientific Accelerator

The espers of Academy City are classified into six levels, where "Level 0" lacks power while "Level 5" possesses an overwhelming amount. Of the several million espers residing in Academy City, only seven of them have attained Level 5, and ranked highest among them is the one known as Accelerator. Toaru Kagaku no Accelerator focuses on the strongest Level 5 after he protects the cheerful Last Order at the price of much of his power. Recovering at the hospital, Accelerator has led a relatively quiet life until he ends up saving the life of Estelle Rosenthal, a mysterious girl carrying a photo of Last Order. Unfortunately, Accelerator now finds himself dragged into a new conflict in the form of a sinister organization called Disciplinary Action which plots to use Last Order for a dangerous mission. Now that they have set their plan into motion and are in pursuit of the young girl, it's up to the world's most powerful esper and his newfound companion to protect Last Order and defend Academy City in the process. (Source: MAL Rewrite)

Full Metal Panic!

Sousuke Sagara, a seventeen year old military specialist working for the secret organization MITHRIL, has been assigned to protect the latest "Whispered" candidate Kaname Chidori. To complete this task Sousuke will have to deal with enemies from his past as well as the occasional panty thief. Unfortunately for Sousuke, the toughest part of his mission isn't only protecting Miss Chidori but also getting used to living an average High School students life, no easy task for someone raised on the battlefield. (Source: Anime News Network)

ALDNOAH.ZERO

In 1972, the Apollo 17 mission found a hypergate to Mars on the surface of the moon. Upon landing, astronauts discovered a enchanted utility later referred to as 'Aldnoah', giving the astronauts a status of superiority. Soon, many humans have relocated to Mars, and have adapted to the name 'Martians'. After Princess Asseylum, a royal Martian princess, descends onto Earth in an attempt to create a treaty between both planets, a war breaks out between Earth and Mars, and Martian soldiers begin to descend from the sky, riding steel giants, intent on exterminating humanity. (Source: Anime News Network)

Gurren Lagann

In a far away future, mankind lives underground in huge caves, unknowing of a world above with a sky and stars. In the small village of Jiha, Simon, a shy boy who works as a digger discovers a strange glowing object during excavation. The enterprising Kamina, a young man with a pair of rakish sunglasses and the passion of a firey sun, befriends Simon and forms a small band of brothers, the Gurren Brigade, to escape the village and break through the ceiling of the cave to reach the surface, which few believe exist. The village elder won't hear of such foolishness and punishes the Brigade. However, when disaster strikes from the world above and the entire village is in jeopardy, it's up to Simon, Kamina, a girl with a big gun named Yoko, and the small yet sturdy robot, Lagann, to save the day. The new friends journey to the world above and find that the surface is a harsh battlefield, and it's up to them to fight back against the rampaging Beastmen to turn the tide in the humans' favor! Pierce the heavens, Gurren Lagann!

Rewrite

Rewrite is set in the fictional city Kazamatsuri, where treeplanting and afforestation have caused the city to become overgrown with trees and flowers in much the same way that other cities are filled by buildings. However, while most of the city appears to be rural, there are many traditional city elements as well. While set in a modern setting, the city also gives off a strange sense of nostalgia. Tennouji Kotarou lives here. He's a high school student who has the ability to rewrite his own body; he can become stronger and faster at any time he chooses. He investigates supernatural mysteries with five girls from his school. (Source: VNDB)