Not believing in god doesn't mean that you don't have morals or ethics. Same as being religious does not mean that you do have morals. For instance the concept of Karma is perfectly valid with or without a deity to keep the score. It is just common sense that if you are nice to people, people will generally be nice back to you. Also if you would just be nice to people when you thought you could get something back from the them, other people you interact with would see through you pretty fast. So even without a god it just seems like a good idea to follow the golden rule.
To me it seems atheists are less likely to commit truly horrific crimes than religious people simply because there is no potential payoff after this life that could be used to entice the act. I also think there are fewer beliefs that an atheist would hold so strong that they think it would be worth to do violence against other people to promote them. I don't know of any atheist equivalents to Al-Qaeda, Ku Klux Klan or the current Anti-abortion activists in the USA.
The problems arise when a specific religion tries to inflict a certain arbitrary set of moral rules on the rest of the population. This becomes especially bad when the religion has a majority and start enforcing their rules on the minority. This includes for instance gay marriage or women's reproductive rights. I also find it troubling when it leads to trying to replace science education with theology.
It is even worse when it leads to just straight wanting to not educate children at all, like in the attacks on female schools in Afghanistan performed by the Taliban. Unfortunately this kind of thinking exists even here in the USA as is shown by the Texas Republican Party coming out against teaching children critical thinking. The bottom line is that an ignorant and uneducated person is so much easier to lead than someone who thinks for themselves. Then again perhaps they were right in The Matrix. Maybe ignorance is bliss!