Attack on Titan has Kenny the Ripper, a Jack the RipperExpy mentioned to have once stalked the streets of the Capitol decades prior. His killings are the stuff of legend, with one soldier wondering whether or not he actually existed. The story goes that he slit the throats of over 100 members of the Military Police Brigade and was never caught. Levi confirms this individual did indeed exist: Kenny Ackerman was his maternal uncle, raised him, and later became a Captain in the Military Police's sinister 1st Brigade. It's later implied that many of his killings may have actually been in response to him and the rest of the Ackermans being hunted down by the government.
One of the early Bleach villains counts. Unlike most other hollows, Shrieker is just as bad dead as he was alive. He was a serial killer in life and seemed to simply just really enjoy it. His actions as a hollow are more of the same, just much more creative with his new powers, including sealing the soul of the kid who killed him in a parrot. Needless to say, when Ichigo appeared and ripped out his tongue before curb stomping him, it was incredibly satisfying. Being impaled and dragged to Hell was the cherry on top.
One particularly loathsome Contractor in the second season of Darker Than Black was a serial killer before getting his powers, and while being a Contractor means Lack of Empathy, that actually made him a bit saner and more able to control himself.
In a way, Nick in the first season might qualify. He was killing people to carry out a goal, not just as an end in itself, but his Power at a Price involved a compulsion to untie his victim's shoes, and so he kind of fit the "killer with a calling card" idea.
There's a ton of them in Deadman Wonderland; they all eventually end up being forced to murder each other. A few are excited about that.
Descendants of Darkness has played with this. In the Kyoto arc, Muraki goes on a serial killing spree, partially to draw Tsuzuki's attention, and partially to try and create a Frankenstein monster styled body with which to resurrect his hated brother so he can kill him with his own hands. Did I mention this guy's a psycho?
He's also behind the serial vampire murders that constitute Tsuzuki and Hisoka's first case together (Nagasaki), and the cruise ship disappearances they investigate later, which turn out to be organ farming. This is kind of his thing.
The Psychopathic Manchild named "Old Cho" from Domu: A Child's Dream psychically controlled 29 people into "committing suicide" all within three years, so he can take one possession of theirs as a trophy.
Lucy, the protagonist of Elfen Lied has killed people ever since she was young, ranging from having a place to eat and sleep for a couple of nights to the person looking at her the wrong way. She's a disturbing combination of Visionary as she's led by her DNA Voice to kill and Hedonistic due to her numerous fits of glee and laughter as she butchers people. The news reports even label her as such.
One early chapter of Franken Fran has Fran being brought on as a consultant for a serial killer case where the killer dumps severed body parts all over town (that, according to DNA tests, all come from the same person, despite the fact that this should be impossible.) Eventually subverted, as there is no killer. All the body parts indeed come from one person... who is suffering from a massively hyperactive malignant cancer that causes her to sprout entire extra body parts and organs, and the ones leaving the body parts everywhere are most likely her parents, who were cutting them off of her.
Barry the Chopper is a comically violent serial killer even after his death. That said, the images of his backstory are rather unnerving, and the only reason he stops killing is because of his involvement with the various conspiracies.
This series also gives us The Slicer, who (like Barry) is Animated Armor, created to guard Lab 5 following the execution.
Scar is of a different (and often overlooked) variety. He only targets state alchemists with the motivation of revenge for the massacre of his people. This makes him a "mission-oriented" serial killer. He becomes more of a sympathetic Anti-Villain and then Anti-Hero over time.
Goth follows a pair of murder-obsessed high school students who track down serial killers to admire their (often gruesome) work.
In Ibitsu, Kazuki is horrified to learn, far too late, that he's not the first person approached by the "Strange Lolita" killer. The others who became the Strange Lolita's "older brothers" were never heard from again.
Yoshikage Kira, the Big Bad of JoJo's Bizarre Adventure: Diamond is Unbreakable, kills women for their hands which he has a strange fetish for (he thinks of the hands as his "girlfriends" and he seems to show no interest in the rest of the body). He is all the more dangerous because his ability leaves no evidence, and he will kill anyone who comes in between him and the quiet life he wants to live.
Angelo Katagiri was arrested at the age of 12 for robbery and rape, and his crimes became progressively more violent as time went on. 20 years later, he was sent to death row for the rape and murder of three teenage boys, and later escaped from prison and went on a killing spree using his Stand before being defeated by Josuke.
Vento Aureo had Cioccolata, a hedonistic-type killer who videotaped all of his victims, who even Diavoloconsidered a monster. As a teenager, he volunteered at a retirement home and would murder old people by drugging them or driving them to suicide through verbal abuse. Later in life he became a surgeon and would intentionally misdiagnose healthy people with illnesses and murdered them on the operating table, reducing the anesthesia so they'd wake up as he killed them.
MPD Psycho centers around the protagonist, who attempts to use his multiple personalities to track and thwart serial killers. Since one of his personalities is itself a serial killer, it goes without saying that things at times can get complicated.
With all the seemingly random killings in StrikerS Sound Stage X of Magical Girl Lyrical Nanoha, this was what the investigators originally thought the Mariage Case was about. However, it soon became clear that Mariage wasn't a serial killer but a group of undeadsuper soldiers seeking the whereabouts of their king so they can begin a new war, all orchestrated by someone else as part of a terrorist scheme.
Johan Liebert, the Monster. He even manipulated other killers into doing his work for him, most of whom also ended up dead. Johan is an unusual example in that it is debatable whether he has a compulsion to kill, since he shows that he can stop whenever he wants, and his traumatic childhood is revealed to have happened to someone else. It should be noted that having these false memories is the only sign of anything resembling insanity; all of his killings and manipulation may be motiveless and insane, but Johan himself comes across as terrifyingly sane (with the exception of one Freak Out!).
Also, he does not appear to get any sort of benefit from killing; he shows no signs of getting a thrill or sexual pleasure from his acts, nor does he seem to get any kicks from domination, and the killings are usually carried out as pragmatically as possible (no wasting time through torture, etc.), which suggests that his use of other people to kill might be simple expedience rather than enjoying his ability to manipulate. In addition, with many of his victims, there is no financial gain or any real progress towards whatever plan he may have at the time, making their deaths pointless. The lack of any recognisable motive is the main reason why he's widely considered Nightmare Fuel incarnate.
Mother Keeper has two. Lint is mentioned on multiple occasions to have been a serial killer before becoming a mother keeper, though little is said about his crimes. The second one is Graham Gregson who killed the real Graham Gregson, along with the man's entire family. He later also murdered Silas and everyone working for him.
Murciélago focuses on Serial-Killer Killer Koumori Kuroko, who herself murdered 715 people before being caught. Her targets are serial killers too dangerous for normal police, such as a man who killed an entire train's worth of people with Razor Floss and a giant wrestler doped up on Psycho Serum.
Gaara constantly murders anyone who gets in his way, all because he believes that this is his sole purpose. Though he and his known victims are combat personnel and thus 'fair game', sort of, they were killed outside of combat situations. One notable instance would be the time Gaara killed two shinobi gamblers trying to get him to take a fall in the Chuunin Exam fights.
HIDAN. Kills for pleasure, cool down time between kills, likes to torture. He may even be named after Hedonism, one of the above categories.
Orochimaru is, or rather was, a straighter example; he fled the Leaf village after being exposed as a serial killer who had abducted and killed close to a hundred ninja, civilians, and babies to perform gruesome human experiments, though a number of these were technically unintentional in that he was usually trying to find safe ways of performing said experiments on himself and therefore wasn't really wanting them to die (not that he gave a crap if they did, it's just that their deaths were beside the point — plus, he seemed to be really enjoying himself).
Pandora Hearts gives us Illegal Contractors, people that forge a Deal with the Devil in the hopes of changing the past. Part of the bargain requires them to sacrifice victims to their Chain, and many develop patterns or preferred victims over the course of time. The most notable examples include the mysterious Head Hunter and the Red-eyed Ghost — the former beheads victims and turns out to be both Humpty Dumpty and the Queen of Hearts, while the other is in fact Xerxes Break in a surprising example of a Serial Killer with a Sympathetic Murder Backstory.
Kabuto from Parasyte. We don't know much about him, since by the time he first appeared he was already in jail, but a few flashbacks show that he used to be a big fan of mutilation, cannibalism, and necrophilia. He is brought to help the police catch parasites because he has the ability to see who is infected. It's implied to be because he sees other humans the same way parasites do — but at least the parasites need to eat humans to survive. He pretends that, deep down, everybody is like him, and he's just the only one who doesn't try to suppress his true nature.
Naoki Urasawa, the creator of Monster, has another manga called Pluto, in which he manages to turn the titular character, a big, goofy-looking green cartoon robot with horns from the classic Astro Boy series, into a genuinely terrifying serial killer figure.
One killer in Q.E.D. is a person who graduates from MIT's mathematics department implied to suffer from a bit of delusions of grandeur, wanting to be remembered as the department's ace by killing three other aces from MIT's aerospace engineering, quantum mechanics and genetic engineering department in Touma's year, making reference to e, i and π in all murders and planned to kill himself to "complete Euler's Identity".
Udo Jinei, the first major villain in Rurouni Kenshin, is introduced as this, committing multiple murders in the past 10 years under the name "Kurogasa" ("Black Hat"), and targeting politicians who previously fought on the side of the newly-established Meiji government during the days of the Bakumatsu. According to his M.O., he always sends a message to his target in advance, telling them the exact day and time he's going to strike, and he always gets his target no matter how many guards the person has in place. In the anime, it's also noted that women and children have been among his collateral-damage victims during his career. It's revealed that Jinei was actually hired to perform all those murders by a crooked politician looking to make his rise to the top of the government. In the manga, while dying after committing suicide following his loss to Kenshin, Jinei admits to having been hired to commit the murders; the anime doesn't reveal it until much later, when we're introduced to the same politician, who currently has Saito on his payroll (at least, so he thinks).
Cho Hakkai (AKA Cho Gonou), one of the main characters in Saiyuki, is a mass revenge serial killer who goes Ax-Crazyyandere after his twincest older sister/lover is sacrificed by his village as an offering to the local demon king, leaving half of the village and most of the demons clan dead in the aftermath.
Tokyo Ghoul has several, primarily Ghouls with unusual feeding patterns.
Shuu Tsukiyama stands out from other Ghouls due to his unusual feeding patterns imitating a human Serial Killer. He is a Picky People Eater to the extreme, and selects potential victims based on them having some exceptional or beautiful trait. At one point, Investigators discussing the "Gourmet" case are able to discern several important events taking place in the series based solely on him breaking from his strict patterns of behavior and feeding on victims that aren't up to his usual standards.
Yuujirou Utsumi, from the second light novel. A businessman famous for his generous nature, he turns out to be a vicious cannibal that enjoys preying on young women. His adopted children are ghouls that he raised to commit the murders for him, while Utsumi himself turns out to be human. By the time he's caught, he's already terminally ill and no longer capable of forcing the children to do his bidding.
In the sequel, the ghoul Torso is explicitly described as a serial killer. A deranged loner, he works as a taxi driver and kidnaps women with scars to become his dismembered "lovers". He is considered disturbing even by others of his kind, and his home is a Cannibal Larder filled with the bodies of his victims.
Underdog: Naoto's first opponent, Masaya Hiuchi, is an 18 year-old who was just recently released from a mental institution after brutally murdering several of his female classmates in middle school. His first actions in the tournament show that he's already up to his old tricks.
Hero Killer Stain is a mission-based serial killer who, like his alias says, targets superheroes. He believes that society's class of superheros are corrupt glory-hounds who are heroes in name only, and have completely lost sight of the virtues that he believes make people real heroes. He used to be an advocate for societal reform so heroes are self-sacrificing altruists and not celebrities, but at some point he made a flying leap off the deep end and now murders heroes and supervillains with the same lack of mercy. However, he still does rigidly stick to his belief system, and spares potential victims if they manage to match his standards of what a proper hero should be.
Himiko Toga appears to be a Hedonistic type. Her quirk, like Stain's, activates when she drinks blood. Stain, however, only drinks blood as part of combat and not necessarily as part of his murderous urges. Toga, on the other hand, seems to get sexual pleasure from murdering and draining her victims.
Dabi is implied to be one, since his introduction is coupled with a news article about several charred corpses.