Masumi Takanagi is normal 16 year-old boy, that is until one night, he dreams of an mysterious man cutting off his hand with a scythe. Then he wakes up to the sound of his alarm clock, and finds his hand bleeding. Now strange things are happening and his seemingly woundless hand continues to bleed. What will become of Masumi and his mysterious hand?
(from B-U)

Nagasawa was just an average student... until one night he's bitten by a large, mutated rat on the way home. He's quarantined in the hospital for a while, but when he's released, all seems normal. But soon he's drawn to a man, that bears similar mutations to the rat, and Nagasawa kills him with ease. It turns out that Nagasawa is infected with a disease called "Nightshift" and he's a special case that let's him fight the insane infected, and he's employed my a medical agency to do just that.

The world has been destroyed and twisted due to the actions of one man – at least, that's what Dextera has been told. With grotesque monsters roaming everywhere, he is ordered by the Archangel of the Church of Melct to purify the mad god who dwells in the Neuro Tower; only then can Dextera atone for his sins...
(Source: anime-planet)

From Kindan no Aku site:

While playing a ritual-like children's game called "Persona", students
are knocked unconscious. While asleep, they encounter a man named Philemon who bestows several Personas upon them. When they wake up, the youths discover they can summon Personas.

A cataclysm has destroyed the cities and empires of men and disfigured the spirit of humanity. In this nightmare, it falls to him to descend a mysterious tower in search of absolution. Is the angel correct that he is responsible for the destruction of the world, and what can he do in this monster infested world to redeem himself?

Based on the Saturn/PSX/PS2/Wii game Baroque.

After the great war of the late 1990s as Japan begins construction on a new capital city, earthquakes cause massive destruction and rumors of demons have begun to emerge. The protagonist receives a warning and a demon summoning program.

The colourful story of Aya, Hina, Kei, and their classmates, trying to figure out the mystery behind Risa's sudden disappearance. It all begins with the discovery that her disappearance haves some correlation to the online dating site called "Amore." Hina proposes that they should try out the site first-hand themselves, and upon doing so, they encounter something completely unexpected?!