Paul's importance to Christianity, and hence, to world history, can be seen in three areas. First, with respect to the book that stands at the foundation of the Christian religion, the New Testament. Without Paul, the New Testament would be radically different, if it had come into existence at all. The New Testament contains a total of 27 books written by early Christian leaders for other Christian communities and individuals. Of these 27 books, 13 claim to be written by the apostle Paul (although scholars think that some of these 13 are pseudonymous, written by followers of Paul in his name). One other book--the epistle to the Hebrews--was accepted as part of Scripture because early church fathers thought it was written by Paul. One other book--the Acts of the Apostles--was largely written about Paul. That means that 15 of the 27 books, in one way or another, are directly tied to Paul. And that's not counting the books, such as the epistle of James, that appear to be reacting to Paul's teachings, or others such as 1 Peter or the Gospel of Mark, which appear to be influenced by his ideas. All told, it is safe to say that without Paul, there would be nothing like the New Testament as we know it today.
Second, with respect to the development of Christian beliefs and theology: without Paul, the distinctive teachings of Christianity may never have developed. According to our most reliable ancient records, Jesus preached about the coming of God's kingdom, when God would overthrow the forces of evil and establish a utopian kingdom here on earth, to be ruled by his special representative, the messiah.
Paul, however, transformed this proclamation of Jesus to the proclamation about Jesus, teaching that what really mattered for a human's relationship with God was not repentance from sin (Jesus' own emphasis), but the death and resurrection of Jesus himself. Anyone who trusted Christ's death and accepted the fact of his resurrection would be right with God, and so would enter into God's kingdom when it arrived. And most important, this was true of all people, whether Jew or Gentile. For Paul--and this was a radical teaching at the time, even if it seems commonplace today--a person did not have to become a Jew in order to be a Christian. For in Christ, God's promises are fulfilled to all people, both Jew and Gentile, on equal terms; it is through his death that people are reconciled with God.
Third, with respect to the spread of Christianity: without Paul, the Christian mission, which eventually overtook the entire Roman empire, may never have happened as it did. As one of the earliest, the best known, and arguably the most effective of early Christian missionaries, Paul established churches in key urban areas of the northern Mediterranean, especially in Asia Minor (modern Turkey), Macedonia, and Achaia (modern Greece). These churches then grew and spread, leading to the Christianization of many of the provinces of the Roman Empire. It took several centuries, but eventually this new religion became the official religion of the Empire itself.
What would have happened had the empire never converted? The vast majority of people living in it would have remained polytheists; and Christianity would have remained a sect within Judaism--a group of Jews who believed that the Jewish messiah had come for the Jewish people. To be a Christian, in other words, one would first have to become a Jew.
If Christianity had remained a Jewish sect, rather than a world religion, it would never have taken over the empire. The empire would have remained pagan. The Christian church would never have become the dominant religious, cultural, social, political, economic institution of the Western world. The entire history of the Middle Ages, down to the Renaissance (imagine all of the art work and literature involved!), to the Protestant Reformation, into the modern world--where some two billion people are in one way or another identifiably Christian--none of this would have happened.
What would have happened had Paul never lived? One could argue that the vast majority of people who today call themselves Christian would still be worshiping the gods of Greece and Rome, and Christianity would be one of the small sects within Judaism, with little impact on the world around it.