Generally, those who were not physically or sexually abused who turn to serial homicide as a means of entertainment are highly imaginative people who spend long hours alone while growing up formulating all kinds of exciting fantasies. As they grow older their fantasies expand and enter territory that is disturbing but offers them a sense of control over those they dislike for some reason or other. In many cases, this fantasy further evolves and enters the realm of paraphilia.
Once a paraphilia is thought of and explored by the person, it can become attached to their sex drive and they become addicted not only to violent fantasies (where they get to be the alpha male and untouchable) but paraphilic fantasies that may involve rape, bondage, and necrophilia.
Why does the sexual element of the fantasy become increasingly taboo? The average psychopath is easily bored, and the previous and less taboo fantasy grows old on them. Ted Bundy explained in his last interview with Dr. James Dobson that he had become addicted to regular pornography and gradually worked his way up to being addicted to rape and bondage pornography. He explained how he had become so addicted to the fantasies that he just had to try them for real.
Now, there are plenty of people who are addicted to pornography and violent fantasies that do not become serial killers. The main difference is that those who do make these fantasies a reality have either muted or nearly non-existent empathy. Neuroscience has detected a major difference between brain activity in the prefrontal cortex of a psychopath and those who do not qualify for the diagnosis. A psychopath has trouble processing emotions and this bleeds over to how they process emotional cues from others. Another thing that studies have revealed is that psychopaths do not react with fear as normal people do when they are informed that they will be jolted with electricity after a countdown has ended. Normal people began to sweat it while the psychopaths registered no changes in heart-rate and such.
Another factor is a history of failure or superficial achievements.
What is not true, as some people seem to think, is the notion that serial killers have no emotions at all and that they view all people as objects. Typically there is a temporary disconnect in favor of the fantasy, so that they change how they look at their victims, varying from the way they view someone they know well, which is likely were the myth comes from.
There is no all-encompassing answer to the question, though, so please note that these things only apply to certain situations. Not all serial killers are psychopaths, for example.
One thing that I doubt is the claim that there are serial killers who have never been traumatized in some way or another. Others might fail to see the trauma in their past because it is not related to physical or sexual abuse. There are other forms of abuse, such as psychological abuse from parent figures or religious establishments.