One of the arguments I've heard repeatedly - and recently - is that the existence of evil in this world shows that God does not exist.
The argument is essentially parallel to this: "I've heard that there is a guy named Andrew who stabs people with knives. Stabbing people with knives is evil, therefore Andrew doesn't exist."
It may be that this argument is evidence that Andrew is an evil person (or is a heart surgeon), but by no stretch of the imagination is it an argument that Andrew does not exist. In the same way, the existence of evil in this world is not evidence that God does not exist.
I think people can legitimately look at evil and ask whether God is good and wonder how a good God can permit evil, and if they do this I think they will find answers to those questions since the whole Bible is essentially about that topic. All that, I think, falls into the category of reasonable questioning, but if they use the "evil-means-no-God" argument, then all they do is make themselves look exceedingly foolish.