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.

Durarara!!

In Tokyo's downtown district of Ikebukuro, amidst many strange rumors and warnings of anonymous gangs and dangerous occupants, one urban legend stands out above the rest—the existence of a headless "Black Rider" who is said to be seen driving a jet-black motorcycle through the city streets. Ryuugamine Mikado has always longed for the excitement of the city life, and an invitation from a childhood friend convinces him to move to Tokyo. Witnessing the Black Rider on his first day in the city, his wishes already seem to have been granted. But as supernatural events begin to occur, ordinary citizens like himself, along with Ikebukuro's most colorful inhabitants, are mixed up in the commotion breaking out in their city. (Source: MAL Rewrite)

Darker than Black

In Tokyo, an impenetrable field known as "Hell's Gate" appeared ten years ago. At the same time, psychics who wield paranormal powers at the cost of their conscience also emerged. Hei is one of the most powerful of these psychic agents, and along with his blind associate, Yin, works for one of the many rival agencies vying to unlock the mysteries of Hell's Gate. (Source: Anime News Network)

Boogiepop and Others

There is an urban legend that children tell one another about a shinigami that can release people from the pain they may be suffering. This "Angel of Death" has a name—Boogiepop. And the legends are true. Boogiepop is real. (Source: Seven Seas Entertainment)