"If no one believed in God how do you think the world would be today?"
Pretty much the same as it is. The reason it would be the same is because people/societies would still make laws that were for the protection/survival of the particular society.
There would be wars and skirmishes because the diversity of man allows for some to be greedy and wanting territory belonging to others.
There would still be crime of similar sorts as now because various individuals still wouldn't respect the rule of law or the rights of others.