Locke the Superman: New World Command (1991)

In feudal Japan, half-demon twins Towa and Setsuna are separated from each other during a forest fire. While desperately searching for her younger sister, Towa wanders into a mysterious tunnel that sends her into present-day Japan, where she is found and raised by Kagome Higurashi’s brother, Sota, and his family. Ten years later, the tunnel that connects the two eras has reopened, allowing Towa to be reunited with Setsuna, who is now a demon slayer working for Kohaku. But to Towa’s shock, Setsuna appears to have lost all memories of her older sister

Earth has been populated by thousands of aliens from all over the galaxy. While all the other aliens are aware of their presence, it is a secret only from the Earthlings. Baka, the prince of the planet Dogra, crash lands on Earth and loses his memory. He forcibly moves in with Yukitaka Tsutsui, a first year high school student who had just moved out on his own. The normal life he once knew is quickly pulled away as he becomes the target of the prince's torment.

When Saki Morimi gets into trouble with the police while in Washington D.C., she is helped by a Japanese man who calls himself, Akira Takizawa. Akira has only two things, a gun and a cell phone loaded with 8.2 billion yen in digital money.

Lingalind is a land enclosed by the Wall. The Wall covers, protects, cultivates, and nurtures the land. One day in Edger, a village on the outskirts of Lingalind, a mysterious man named Back Arrow appears. Arrow has lost his memory, but he claims that all he knows is that “I came from outside the Wall.”

Jotaro Kujo is a popular high school student – at least until that day when he thinks he is possessed by a ghost, which is why he locks himself up. During a fight between his grandfather and his grandfather’s friend Muhammad Abdul, he notices that the ghost is his “Stand”, named "Star Platinium", his fighting aura. Later, his mother also gets such a “Stand” and thus falls ill. Jotaro learns that a man named Dio Brando, who was defeated by Jotaro’s great-great-grandfather a hundred years ago, is to blame. He joins his grandfather and Abdul to destroy Dio once and for all.

In a world where memories can be stored like computer data, a young man named Kaiba searches for his lost memories and discovers a connection with a mysterious girl.

Oz Vessalius, heir to one of the duke houses, has just turned fifteen. His life is rich and carefree, darkened only by the constant absence of his father. At his coming-of-age ceremony, however, everything changes. For no reason that he can discern, he's cast into the prison known as the "Abyss", only to be saved by a "chain" known as Alice, the bloodstained black rabbit. It is unknown why was he cast into Abyss, how does Alice factor into it all, and what does the organization known as "Pandora" want with him.

Forty years ago, the minds of Paradigm City's inhabitants were wiped clean of all recollections of the past. Now, ruled by a powerful corporation and cut off from the rest of the world by desolate wastelands, Paradigm has become a virtual police state where Negotiators like Roger Smith keep the wheels of progress, commerce, and society turning.

In the year 2024, the world has collapsed. Grotesque monsters lurk amongst the ruins of Japan, while remaining people scrape together what they can to survive. Kiruko, an odd-job girl in Nakano, accepts a mysterious woman's dying wish to take a boy named Maru to a place called Heaven. Maru is convinced that there will be a boy there who looks exactly like him.

The anime follows a salaryman who has a chance meeting with a girl named Ai on the train. They begin to meet every Monday on the train, with the man serving as her bodyguard on the crowded commute while they chat.