One important reason for the spread of Christianity was the evangelical missions of Paul of Tarsus. Paul, originally called Saul, was perhaps the one person most responsible for the spread of Christianity throughout the Roman Empire. Paul was not one of the original 12 Apostles of Jesus Christ, whose life and teachings are the basis of the Christian religion. Paul originally persecuted the followers of the teachings of Jesus until he had a conversion experience after which he became a strong follower of Christ and began his evangelical missions. Paul, a Greek speaking Jew from Asia Minor, went on three missions covering 10,000 miles over the course of thirty years. He traveled through Palestine, Syria, Asia Minor, Macedonia, Greece, and Rome, establishing Christian communities in each area. Paul made the decision to spread the Christian faith to non-Jews, which helped establish the Christian religion throughout the Roman Empire. The Roman system of roads allowed the Christian message to travel quickly from one place to another. The fact that Paul spoke Greek and was a Roman citizen also helped Paul in his travels to spread the Christian religion.
The most usual explanation for this is that Christianity had a message that resonated with many people in the Empire in the centuries after the death of Christ.
What this school of thought argues is that Christianity's message was so different from the messages of the pagan religions that dominated Rome. It says that these differences made Christianity appeal to a wide variety of people. Doctrines such as the idea of the value and equality of each human being in the eyes of God were comforting and inspiring enough to catch on.
Of course, the actions of Constantine in becoming Christian helped, but this seems to be more of a result of the spread of Christianity than a cause of the spread.