Gosenzo-sama Banbanzai!

The Yomota family is small and typical: father Kinekuni (42), mother Tamiko (38), and son Inumaru (17). One day, a beautiful girl appears at their front door, calling herself "Maroko Yomota," granddaughter of Inumaru who travels back in time with a time machine to visit her ancestors. Even with Tamiko's strong objection, Kinekuni and Inumaru welcome her to stay with them, and the structure of a happy family has begun to collapse. (Source: Anime News Network)

FLCL

Naota is a detached sixth grader afflicted by the pangs of puberty. He's fooling around with his brother's ex-girlfriend when a crazed girl on a motor scooter runs him over, brains him with a bass guitar, and moves into his house. This pink-haired girl, Haruko - who claims she's an alien - hurls Naota into the middle of a mega-corporation's secret agenda. Oh, and now giant battling robots shoot from his skull. Mix in mind-bending animation and tunes that echo through your cerebellum to top off the trip that will have you falling hard for FLCL</i>. (Source: Funimation)

Akira

It's the year 2019, thirty-one years have passed since the start of World War III. A top-secret child with amazing powers of the mind breaks free from custody and accidentally gets a motorcycle gang involved in the project. This incident triggers psychic powers within one of the gang members, Tetsuo, and he is taken by the army to be experimented on. His mind has been altered and is now on the path of war, seeking revenge on the society that once called him weak. (Source: FUNimation)

Neo Tokyo

1) Labyrinth Labyrinthos A girl and her cat fall through a looking-glass into a dark labyrinth full of strange people. 2) Running Man In the distant future, a tough racer uses his psychokinetic powers against his opponents during his final race. 3) The Order to Stop Construction A snooty salaryman is sent by his bosses to the jungle to stop a completely automated construction job, and spends several days there arguing with the robots. (Source: Anime News Network)