Well this thread needs someone actually thinking about it.
Our very first civilizations were based on religion, at least the big empires. There would never be an egptian empire. So no pyramids at the Nile. Likely the Egypt and the entire ancient world would be structured on state cities from north Africa to eastern Asia. Regions like India or Japan never would come into being empires for they were based on religion.
I'd figure out the states that developed philosphy first would be very well positioned. Greece, a buddhist-like India and China would grow and their cultures would dominate most of Eufrasia. if the Roman Empire still existed it would work like a Bigger Greece for all purposes and unlikely to face crisis like the one christianity brought to it. Slavery and a city-driven economy would persist unless some anti-slavery philosophy became strong enough. There'd be no Arab Empire.
Assuming nations like China, Inda and Greece successfuly avoid being destroyed by mongol and germanic people, a renaissance-like period would like develop before the 1000-s (at least in our calendary). America would be easily colonized since there would be no civilizations there (Incs and Astecs were based in religion). There would be no cruzades or inquisiton in the 1500-s, time by which we'd be reaching today technology levels.
Well there you have it. Technology would develop much faster and we'd live in a much more liberal world. But who knows what else could happen? I'm pretty sure mankind would find another reasons to battle over the course of history and still today, and who knows for sure if history would be more or less bloody. What I can say with nearly certain is that it would be less redundant. But a world developing a different way could not escape Cold War-like nuclear devastation like we did by a strike of luck. Who knows.
I hope some of this actually made sense.
