So as an actual atheist, let me describe what I think the world would be like without religion.
1. No one would kill each other over which imaginary friend is more "real".
2. Parents wouldn't be allowed to deny their children life-saving medical care on the basis of "God wants them to be sick!"
3. No religions means no religious objections to birth control Greater access to birth control would likely reduce overpopulation and poverty.
4. Given that people would know that this is the one and only life they get, perhaps they'd spend more time trying to make this world better and less time worrying about the next world.
Humans are human, and it is in our nature to fight each other. But it's silly to think we'd kill one another over things like competing scientific theories ("Science damn you!"), because those have the advantage of being provable and verifiable, which religion, by its very nature, is not.
Now, getting down from my soapbox...
There's not too many ways I can think of where we end up with a truly secular world. A stronger trend towards science and learning during the Enlightenment would help, as would a very charasmatic atheist philospher in the early 1800's era. Someone like Marx, perhaps, only without the silliness of Marxism.
But even then all we'd likely end up is secular versions of Europe, Australia and North America. I could see reduced religion in places like Africa, Asia and South America, but I don't know if there's any real way to tweak time so you end up with a secular world by 2008.
By 2108, on the other hand... well, I can dream.