http://news.bbc.co.uk/2/hi/science/nature/3013146.stm
So what would happen if Constantine didn't declare Christianity the official religion of the Empire? This isn't a "no Christianity" what-if, mind you - the religion was already fairly well established and widely spread. But without official sanction, I doubt it would have spread as thoroughly to the ends of the Empire. The Western Empire would likely still have fallen, but perhaps its remnants would not be so completely unified by Christian culture. Or alternatively, by centralized Catholicism - Christianity might have remained a more diverse religion with no one branch managing to basically eliminate the others.
So what would happen if Constantine didn't declare Christianity the official religion of the Empire? This isn't a "no Christianity" what-if, mind you - the religion was already fairly well established and widely spread. But without official sanction, I doubt it would have spread as thoroughly to the ends of the Empire. The Western Empire would likely still have fallen, but perhaps its remnants would not be so completely unified by Christian culture. Or alternatively, by centralized Catholicism - Christianity might have remained a more diverse religion with no one branch managing to basically eliminate the others.