Pink for anime. Green for manga.
The Disastrous Life of Saiki K is the only psychic anime besides Mob Psycho 100 that you want to watch. Most anime comedies don't make the cut because a lot of writing gets lost in translation but Saiki K's comedy is timeless.
Kusuo Saiki is a highschooler who was born with telepathy and omnipotent powers alike. Think One Punch Man, or Mob Psycho 100. He struggles everyday to fit in as God in a teenager's body, and faces challenges that could give away his psychic status. The humor is based almost entirely on subverting tropes or situational absurdity, and the delivery never lingers for too long. Besides the low budget animation, I don't have anything bad to say about this show.
I Am a Hero, an apocalyptic horror manga. Zombie outbreak stories are typically weak and nothing more than "chipping off the expendables" violence porn, but not I Am A Hero. I Am A Hero (transliterated Eng→Jap) is an outbreak serial done well, even for those who aren't fond of the genre (like me.)
Hideo Suzuki is a man who works as a mangaka and leads a fairly
deadbeat life. A zombie pandemic gradually takes over Japan, and Suzuki learns to adjust to a life of survival when he loses his girlfriend to the outbreak. He also handles his survival whilst dealing with delusions and paranoia, which is a major aspect of Suzuki's characterization that gets dropped in the movie.
If you enjoy realistic and natural slow-paced stories, you might like I Am A Hero.
Dorohedoro, an experimental CG action comedy. I tried to recommend this anime to a fellow anime club member asking, but the best I could summarize is that it's "about a resident in the Hole who gets his head turned into a lizard and seeks out for the perpetrator." Best "3D animated" anime out there.
Boku dake ga Inai Machi (Erased), a thriller mystery. Since it's a thriller, I'll just keep the summary short. MC (24) involuntarily can travel through time. It's never explained why it happens, though its a common motif the mangaka works with as seen in his other manga, "For the Kid I Saw In My Dreams," as a way of exploring his characters. Anyway, these "time traveling" periods usually take a few hours or minutes back into the past with the presumption that there's "something to be fixed" or is in the MC's power to change. One day, he travels all the way to his grade-school years, realizing he was sent back in time to solve the murder of his classmate.
Season 1 of Bokusatsu Tenshi Dokuro-chan, a magical-girl comedy (not too unlike the humor style of Urusei Yatsura) translated to "Club-To-Death Angel Dokuro." MyAnimeList may hate it, but I! Don't! Care! Besides, I don't take flak from chin-high otakus. Dokuro-Chan is an angel who comes from the far future assigned to kill the pedophile who invents "immortality technology" in 20 years, which prevents all women from developing past the age of 12. She ends up living with his 13-year-old self and instead of killing him, she distracts him from discovering said technology. It is crude, annoying, plotless, and full of bloody slapstick. It's solely a guilty pleasure and more of a "novel experience," so I'm begging you to just watch this on your own time if you care about your relationships. Also, avoid season 2.
Inuyashiki Last Hero, a superhero sci-fi.
Ichiro Inuyashiki takes his dog Hanako out for a walk and when he looks up at the stars, he's struck by a UFO and rebirthed the next morning as an indestructable weapon that lives amongst the human race.
Inuyashiki Last Hero never explains the UFO, but only because the series heavily focuses on the philosophy of "Theseus's Ship": if you were remade into wire and metal one day, would you still be the same man that you were yesterday? What defines humanity? If you liked Deathnote, you might like Inuyashiki: Last Hero.