Hariyama-san, Center of the World

Far and away Narita Ryohgo's best series, the Hariyama-san series -- of which there are exactly two books, so far -- effectively consists of short stories in whatever genre he damn well feels like. Hariyama-san himself is an eternal supporting character -- never integral to the action, he is often simply mentioned in passing. He's just in all the stories.
Each volume also has a fourth story that ties all the previous stories together into one big mash-up climax.
The first volume kicked off with a girl spying an axe murdered under her boyfriend's bed and trying gently to ease him out of the place, while he desperately tries to keep her there because he just saw a man running around with an axe outside his apartment. That man had actually being trying to kill the girl, but snuck into a yakuza's apartment across the way by mistake.
Then we get an INSANE magical girl -- she's from the kingdom of magic, but has watched too much anime and is constantly breaking the law and going to Japan to fight evil. But when she attempts to take down some yakuza, they take pity on her, promise her she'll never be made to fight for anyone again, and adopt her.
And then fuck up the magic police who come chasing after her.
Meanwhile, on a distant island, a boy discovers that he's actually the evil overlord, and everyone else on the island is a hero destined to kill him.
Even his girlfriend.

Hariyama-san, Center of the World 2, which I just read, is even more awesome.
Kicks off with a horror story about a taxi driver who picks up the ghost of a murdered girl; she's just about to kill him when she realizes his taxi is from another dimension.

Then we get the tragedy of No. 37564, an ordinary minion in an evil organization...for the fifth time running. Every single time he gets captured and mad scientists finish altering his body, the organization winds up getting destroyed by heroes. Before he gets brainwashed. Consequently he has become the strongest man in the history of time. Fortunately, he has absolutely no ambition, and is content to serve the twelve year old boy who runs the evil organization just like evil organizations are run on TV because he's suicidal and wants to be killed by the heroes. Who No. 37564 keeps fucking terrorizing.

The Don't of the Dead
A hitwoman with a pathological aversion to human body temperature has her dream come true when she finds herself mixed up in a war between Science Zombies and Magic Zombies. The two children controlling the armies turn out be zombies themselves, and totally running the whole thing as a game because they plan to kill her and turn her into a zombie slave. She sort of turns the tables on them, has them make her into a zombie, and adopts them.

The Red Death of Kashiwagi Cross
Opens with a hero No. 37564 beat up cheerily explaining how great heroes are to a totally unimpressed policeman, who eventually points out that this really isn't going to help him plead insanity. Fortunately, Hariyama-san doesn't press charges. (When No. 37564 punched him, he landed on the roof of Hariyama-san's car.)
The heroic chant he constantly repeats turns out to be a product of his brainwashing; the awesomely named Genociders turn out to be working for a mad scientist who betrayed the evil organization No. 37564 worked for (they briefly had a giant robot named Big Massacre, but No. 37564 kicked it. Once.) and when he tries to rejoin them they kill him.
And then he gets turned into a zombie.
And then he gets possessed by the little dead girl from the first story.
And then everyone has a barbeque at Hariyama-san's house.