The problem with a question like this is that it entirely depends on your definition of religion.

There have been atheist states, but you can define religion to include a cult of personality.

There are secular states, but I'm pretty sure that's not what you're looking for.

You can define religion as a shared set of morals and beliefs about the world.

Without having a clear definition, you will get answers from many people pushing their own particular agendas.

Well the communist states definitely we're non-religious and stamped it out. I don't know about earlier history.

Religion is pretty much steroids to a population, and make them more connected and easier to unify. Also they are more likely to see enemies in the ones that they don't agree with. Population morale booster in a sense, even for fighting wars. So a civilization without religion is in that sense missing out.

I think that is one of the reasons the islam spread so good in the middle ages, and Constantinopel chose Christianity for the eastern roman empire.

Interesting question.