How did the Roman Empire facilitate the spread of Christianity?

The structure of the Roman Empire, and the way that it was governed, made it easier for the Christian message to be spread among its subject peoples. This was largely due to the Pax Romana, or Roman peace, an extended period of relative peace and stability that lasted from about 27 B.C. to 200 A.D. During this time, each individual territory of the Empire was given a great deal of leeway in making and administering its own laws while at the same time accepting Roman taxes and military occupation.
Under such conditions, all kinds of religion thrived, most notably Christianity. The Romans were pretty relaxed when it came to foreign religions. So long as they didn't cause serious public disturbances or undermine the authority of the state, then they were tolerated. Sporadic persecutions of Christians did take place in the Empire, but this was always in the context of Roman high politics; Christians were never persecuted because of what they believed, but because their very existence was perceived by certain emperors such as Nero to be a threat to the state.
Try as they might, however, the Romans couldn't stamp out Christianity for good. Ironically, the Romans only had themselves to blame for this. The efficient system of roads and communications they'd built throughout the length and breadth of the Empire had made it so much easier for Christianity to spread and for Christian communities to be established.
Thanks to the extensive Roman road network, Christian evangelists such as Paul were able to travel to the far-flung corners of the Empire, spreading the Gospel, building churches, and converting pagans to the new religion. In building a transport infrastructure that facilitated the relatively speedy travel of people and ideas, the Romans unwittingly assisted the spread of Christianity, the religion that would in no small measure contribute to the collapse of their Empire.