Society finds serial killers horrifying yet fascinating, which is why it should come as no surprise that anime has a ton of serial killer characters. The serial killers in anime are as varied and diverse as ones in real life, but one main difference is that the ones in anime are often a lot more fantastical because they're put in fictional settings. Viewers also have a window to see the motivations and desires of serial killers in anime, making it easier to sympathize with them.
Anime serial killers do what they do for different reasons. Some are driven by a sense of justice that captivates audiences while others are psychopaths who kill without remorse. Their styles of killing also differ, from horrifying and drawn-out deaths to ridiculous anime overkills.
Light Yagami isn't your average teenage boy. He picks up a notebook he finds in the street and discovers that writing someone's name in it causes them to die, and he can control how they die by writing details. Yagami starts off by using his newfound power to save a woman from being attacked, but then the power gets to his head and he starts writing the names of every criminal he hears about in the notebook. By the end of the story, he's killed hundreds of thousands of people.
What's dangerous about Yagami is that he is completely convinced that his sense of justice is correct. He kills without remorse and mercy. While some people in the show support his actions, others find his role as judge, jury, and executioner to be tyrannical.
Yamori - Tokyo Ghoul
Any guy who dresses up like Jason from Friday the 13th has to be a serial killer. This guy is even called Jason, and that's just one example of how Yamori is really creepy. He is thrown in ghoul prison and tortured by a guard. That terrible experience starts him on the path to becoming the most feared person in Tokyo's 13th ward. He terrorizes the whole place, capping it off with a torture session that goes on for 10 days.
At first glance, Yuno Gasai seems like a pretty sweet girl. Yukiteru Amano, the protagonist of The Future Diary, initially thinks so as well. He's thoroughly surprised to find out that this little pink-haired girl is an efficient killer. He's even more surprised to find out that the girl is hopelessly and obsessively in love with him.
To elaborate on her victims would be venturing deep into spoiler territory, but the main thing to learn from her is that psychotic high school girls who are in love should not be underestimated. There's a reason why she's the yandere poster girl, after all.
While Caster from Fate/Zero has a lower body count than his boss, Ryuunosuke, he made this list because he's particularly cruel to his victims. He likes to offer his victims hope, making them think that the pain will be quick or that they will be released. Once they have hope, Caster takes joy in ripping it away. He does this so the pain of his victims is amplified and he can enjoy their deaths more thoroughly.
What makes Caster scary is that he has no qualms about killing children. In fact, in Fate/Zero, he collects hordes of children and ends them because he thinks that's what God wants.