In this essay the varied and probable reasons Paul might write to the Romans are outlined, and brief but important information concerning who the Roman believers were and who Paul was is presented for consideration and illumination on the subject.
To properly understand why Paul wrote his epistle to the Romans, it is necessary to consider the information pertaining to the people involved, to remember the major cultures of the time, and to examine the key themes of the book.
The Roman Christians were a mix of Jewish and Gentile converts who had most probably been converted by the witness of travellers who had been in Jerusalem during Pentecost. Positioned in the hub of the known world, Rome was a bustling city with a full and vibrant culture. The Gentiles in the Roman church would have come from a large variety of backgrounds and would most likely have been the larger people group in the church. Evidence in favour of this and pointing to an important reason for Paul to write his epistle is presented by Thomas Schreiner in his exegetical commentary on Romans:
What tilts the scales in favour of a Gentile majority is other internal evidence in Romans. In Rom. 1:5-6 Paul addresses the readers, identifying his commission as the apostle to the Gentiles, and he specifically includes the Roman readers within the orbit of the Gentile commission. The language should not be pressed to exclude the Jews, but it implies that the majority of the readers were Gentiles.
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The church in Rome was likely raised on Jewish roots through the preaching of the gospel in the synagogues. Thus Gentile Christians would have had a keen knowledge of the OT Scriptures. From the very beginning Jews would have debated Jewish Christians and Gentiles over their interpretation of the Scriptures. Paul needed to demonstrate in Romans that his gospel fulfilled what was written in the Scriptures. His gospel was probably under suspicion in Rome precisely because both Jews and Jewish Christians hotly disputed his interpretation of the Mosaic law and the OT Scriptures.
Paul, so it seems, wrote his epistle to the Romans after penning 2 Corinthians. It is thought he wrote the letter in, or near, Corinth. Paul had not yet visited the Roman believers and he desired to meet with them. The date of this writing is thought to have been approximately AD 57 due to the nature of what Paul was addressing in regards to possible Jewish and Gentile clashes. Claudius had been in power in Rome and had expelled Jews in AD 49 but he died in AD 54.  The Jews had returned: some were also Christians and it is likely they had very different ideas from the Gentile believers. The Roman church probably faced challenges similar in nature to some of Paul’s other “church plants”. 
The composition of Romans has been considered an exposition of Paul’s theology for many years but more recently this theory has been revised by a variety of scholars in favour of a developmental process in Paul’s theology. Whilst other scholars suggest that in writing Romans Paul was summarising objections to his theology which he received in Galatia, Philippi and Corinth. The latter view is fairly superficial; every person is affected by their experiences and will of course express thoughts on the influences by which they have been changed. Those factors must be considered but to say Romans is specifically a backlash to certain objections is to miss the abundance of brilliance contained therein.
Paul was a man who had been moulded by God through his early years, for a task which no other apostle could have fitted into more perfectly. Having grown up as a Jew in a Hellenistic society, trained in a practical trade, followed by impeccable education under Gamaliel, Paul would have had the ability to relate to and converse with virtually every person who he came in contact with. Ladd makes mention of Paul’s background and says we must interpret Paul’s ideas against a very diverse background if we are to understand the historical influences that moulded Paul to be the first Christian theologian.
Marshall discusses how the problems in the Roman church may have been known to Paul and how this was a factor in Paul’s decision to write to them. He also makes mention of Paul’s situation and how that would have affected his writing:
The elements that make up the situation and the relative significance of each of them continues to be a matter of debate. As a letter addressed to Rome, it introduces Paul and his particular understanding of the Christian message to a congregation that he had not founded, although the length of the list of people greeted in Romans 16 indicates that he had a rather good knowledge of the congregation and its problems. At the same time, coming as it does at the point where Paul was about to journey to Jerusalem for what (so far as we know) was the last time, the letter may reflect some of the concerns in his mind at this decisive juncture in his career. The crucial problem is the place of Jews and Gentiles in God’s plan of salvation and their relationship to one another. This practical problem emerges particularly in the closing, practical section of the letter (Rom 12-16, especially Rom 14-15), where the “strong” and “weak” believers appear to be basically Gentile and Jewish respectively. The body of the letter is concerned with the nature of the gospel for Jews and Gentiles, and it takes up in a fresh way the issues that surfaced in Galatians.
Like all of Paul’s letters, Romans contains some of his theology but it is not an exhaustive or conclusive systematic theology. The letter contains what some call Paul’s gospel but that label is somewhat deceptive. Marshall aptly dispels the notion that Romans is simply a summary of Paul’s theology because it is not a comprehensive treatment. Justification by faith is a theme in Romans which has such a profound affect through the ages that we are still feeling the aftershock today. The sovereignty of God and salvation are the other key themes which are found in Romans. Like Justification, those themes arose out of necessity because of the Jewish/Gentile clashes within the church.
The Roman church hadn’t been established by an apostle and it would seem Paul wanted to cement the Roman church with integrity and give them a firm grounding. In doing this he needed to show them who he was as an apostle and that he was worthy of their trust. Paul also wanted to continue to fulfil the commission his Lord had given him.
For God is my witness, whom I serve with my spirit in the gospel of his Son, that without ceasing I mention you always in my prayers, asking that somehow by God's will I may now at last succeed in coming to you. For I long to see you, that I may impart to you some spiritual gift to strengthen you - that is, that we may be mutually encouraged by each other's faith, both yours and mine. I want you to know, brothers, that I have often intended to come to you (but thus far have been prevented), in order that I may reap some harvest among you as well as among the rest of the Gentiles.
Paul’s other motives for making contact can be seen where he expresses his interest in continuing on to Spain with their help and he states his hope was that the church would be an encouragement and a refreshment. Another way he saw they could help him was through prayer.
John MacArthur provides a clear summary of why he thinks Paul wrote his epistle to the Romans:
And so, the letter really was to be an introduction of himself as an Apostle, of his doctrine so they would have no question about it. And so he pens a monumental treatise to establish them in the truth to show that he was truly an Apostle, to give them confidence in himself, and just in case he never gets there, to give them the absolute last word on the gospel of Jesus Christ so they will be established.
In conclusion, the reasons Paul wrote his letter to the Roman believers are diverse in nature and span a considerable range of topics. Understanding why Paul wrote this marvellous letter is central to understanding the book itself. Paul's epistle to the Romans was a self-introduction and proof of apostleship, to ensure their clarity on his doctrine, and to establish a relationship with them, both as a basis for them to have confidence in him, and, in tandem with his doctrine, to establish them in the faith.
Blomberg, Craig L. From Pentecost to Patmos. Acts to Revelation. An Introduction and Survey. Nottingham: Intervarsity Press, 2006.
Ladd, George Eldon. A Theology of the New Testament. Edited by Donald A Hagner. Grand Rapids, Michigan: Eerdmans Publishing Co., 1993.
MacArthur, John. Romans: The Man and the Message. Panorama City, California: Grace To You, 1 March 1981.
Marshall, I. Howard. New Testament Theology. Many Witnesses, One Gospel. USA: InterVarsity Press, 2004
Schreiner, Thomas R. Romans. Baker Exegetical Commentary on the New Testament. Grand Rapids: Baker Publishing Group, 1998.
 Thomas R. Schreiner, Romans. Baker Exegetical Commentary on the New Testament. (Grand Rapids: Baker Publishing Group, 1998), 14-15
 In Romans 1:11 Paul expressed his wish to meet the Roman Christians.
 In Acts 18:2 Paul meets Aquila and Priscilla who were Jews expelled from Rome.
 Craig L. Blomberg, From Pentecost to Patmos. Acts to Revelation. An Introduction and Survey. (Nottingham: Intervarsity Press, 2006), 234-235.
 George Eldon Ladd, A Theology of the New Testament, ed. by Donald A Hagner. (Grand Rapids, Michigan: Eerdmans Publishing Co., 1993), 398-399
 I. Howard Marshall, New Testament Theology. Many Witnesses, One Gospel. (USA: InterVarsity Press, 2004), 305-306
 Marshall, New Testament Theology, 15-16
 English Standard Version
 Romans 15:28
 Romans 15:32
 Romans 15:50
 John MacArthur, Romans: The Man and the Message. (Panorama City, California: Grace To You, 01 March 1981).
http://www.gty.org/resources/sermons/45-01/romans-the-man-and-the-message. Cited 3 Oct 2011.