**John Wayne Gacey ** was important for another reason: he helped implant/reinforce the false image of homosexuals being a bunch of pedophiles. Also, he helped make clowns that much creepier in the public mind.
**Zodiac ** helped make serial killing “cool.” At least, he presented the killers’ self-image of being a badass killing machine. I’m scared to think of how many young men have been influenced by this.
No one has mentioned Jeffrey Dahmer, a man whose name is synonomous with necrophilia and cannibalism. But fictional Dr. Lechter seems to be the patron saint of that phenomenon.
Columbine is iconic as the revenge of the rejected. It’s the teen angst version of going postal. I find it interesting that few people refer to the killers as much as the event. It’s like it doesn’t really matter who did it as much as the fact that it happened.
**Manson ** also helped create an image of the “killer hippie” that contemporaries used to further demonize hippie culture.
**McVeigh ** brought the militia movement into the public view. In that regard he strengthened the governments’ powers and increased the public resistance to those same powers. He, David Koresh and the Ruby Ridge fiasco resulted in terms like “Jackbooted Thugs.”
I would put Orenthal James Simpson on this list. But that’s just me.
This is actually the result of a conscious effort on the part of those most directly affected by the tragedy. The families of the victims, and I believe of the killers as well, publicly requested that the names of EH & DK not be used in the media. And, in an arguably rare showing of public responsibility, almost everyone voluntarily complied. They have now become known simply as “the Columbine killers”.
In this way, the killers were denied the fame which undoubtedly formed a large part of their motivation. We will never know if this collective agreement also hastened the end of the “school shootings” fad/epidemic, but I believe that it did deny the fire a good portion of fuel.
Side note: Michael Moore, notably, ignored this, and used their names blatantly in a largely staged and distorted “documentary” supporting gun control, provocatively titled “Bowling for Columbine” (while he generally ignored what most agree was the killers’ primary motivation – extreme alienation, coupled with self-indulgent anger).
The most influential (barring political leaders like Hitler) would absolutely have to be Jack the Ripper, as the first serial killer who had world-wide press and hysteria at the times of the killings. People were scared that Jack had come to their town as far away as Australia. Most of our basic ideas of what a serial killer are comes from the press reports of the killing and the articles, books and movies that followed – even though most of those things were completely inaccurate. And many later serial killers based some of their acts on what they heard about the Ripper.
Of course, since I run Ripper Notes, the leading magazine about Jack the Ripper, I’m a little biased. 
Regarding others mentioned earlier, no, Vlad didn’t bathe or drink in the blood of his victims, that was reportedly what Elizabeth Bathory did, although it’s likely that those were just legends tacked onto her notoriety and not something that really happened. (Cecil has a column on her but I won’t link since he repeats some of the legends as if they were true without any sort of critical analysis, bad Cecil.)
How could I forget the Tylenol killer? Remember the days before you had to wrestle with umpteen layers of anti-tamper packaging? This guy (I assume it was a man, could be wrong) introduced a whole new kind of fear to the public at large. Everything became suspect. Paranoia became the norm.