Besides simply adopting Christianity, I wonder if a case could be made that the Roman world shaped it's very doctrine. Not in passive ways, like a Christian reaction against Roman ways, or having Roman citizens defect to it... but as a flexing of Roman power to shape Christianity to Roman interests in some degree.
One example might be the Apostle Paul http://www.sullivan-county.com/news/paul/paul.htm who was an early persecutor of Christians and seemed to be funded in this by the Romans although maybe had other motivations. His later life as a Christian convert seems to involve removing some Jewish aspects out of Christianity, and some think this was to make it especially convert-friendly and to seem less foreign to the average Roman citizen. That took a long while, but maybe still is effective today in conversion efforts.
Another example is Constantine, who kind of chaired committees such as http://en.wikipedia.org/wiki/First_Council_of_Nicaea on Christian doctrine. Sometimes described as a passive role in settling esoteric questions, but I think other accounts suggest the stifling of alternative Christian doctrines that would be harder to manage in the context of his empire, such as more mystic and decentralized ones. Could modern Christianity still include echos of things that were "for the good of the Roman Empire"?