From what I can tell, religion or the lack thereof is unquantifiable as an influence on society at large, when it comes to the worst crimes. It's just more sickening when people do the worst things in the name of their particular chosen deity. A 20th century history book is pretty good source material - Stalin and Mao, the worst mass murderers in the history of mankind, were resolutely atheist. Of course, one could call the state ideology a kind of religion in those cases, but it's a stretch. Hitler, number 3 "by the numbers" (although he was a special kind of hideous,) certainly had religion mixed up in his world-view, but could hardly be called a crusader in the religious sense; again, he was more about pure power. It's been argued, on the basis of pure numbers, that lack of religion led to the worst abuses in history.
I personally believe that the combination of an unbalanced political apparatus, an unbalanced sociopathic leader, a virulent ideology, and modern technology enabled this behavior, and religious belief (or more appropriately, the lack thereof,) hardly entered into it.
Similarly, I also believe that people can either give a crap about other people, or primarily serve their own egos/sicknesses/power lust/what have you. And so you can as easily have a pervert "man of the cloth" you can't trust your kid with, as a pervert atheist or secular humanist.
The thing is, people don't understand or believe that a religious man, who espouses religious sentiments, can be capable of evil. It is easy to blame the religion (which, in fact, creates a power conduit in many cases, involving the ideas Miss G mentioned, like the afterlife as a reward system,) or to blame religion in general. And in fact, I think there's a lot to be said for being distrustful of any direct hierarchy in which one is encouraged to internalize fear and guilt (for example.)
But if all religion vanished tomorrow, killers would be killers because they believed in some other ideology -- or even just in some malthusian "population control" movement. Child molesters would find kids without the shelter of a religion. But they would still look for, and find, the kids. We produce a small number of these extremely messed up individuals, and of course, they do disproportionate damage. But I don't think they'd disappear because religion does.
Although I will say that seeing some of the religious posts on this board and elsewhere, I can understand the temptation to think they would.
PFnV