The book of Romans is essential to the New Testament because it is powerfully written and presents the doctrines of the faith as clearly and directly as any other book in the Bible.
This is a book which has impacted readers of it through the centuries.
Luther, in his preface to the Roman letter, wrote: "This Epistle is the chief book of the New Testament, the purest gospel. It deserves not only to be known word for word by every Christian, but to be the subject of his meditation day by day, the daily bread of his soul.… The more time one spends in it, the more precious it becomes and the better it appears." He spoke of it as "a light and way into the whole Scriptures...." Calvin said of it "when any one understands this Epistle, he has a passage opened to him to the understanding of the whole Scriptures." Coleridge pronounced Romans "the most profound work ever written!" Meyer considered it "the greatest and richest of all the apostolic works." Godet referred to it as "the cathedral of the Christian faith." Gordon H. Clark recently wrote of Romans that it is "the most profound of all the epistles, and perhaps the most important book in the Bible.…" Hamilton, in his recent commentary on Romans, calls it "the greatest book in the Bible."
It is a letter written by Paul to a church he had never visited (though he spends several years with them later), yet he addresses many people by their names. So, while it is a personal letter in that regard, it is clearly written to an entire body of believers. He wrote the letter from Corinth and relates sage advice based on what he sees there (plenty of sin, it seems) as well what he thinks the Roman church should be studying and learning. Remember that, while modern Christians have the Bible in its entirety, the New Testament churches generally had little or nothing of the New Testament, so letters like this one really gave them the practical teachings of Jesus which were new and sometimes quite confusing to them.
Several of the most hard-to-understand doctrines of the faith are outlined in Romans better (arguably) than anywhere else in the Bible: justification by faith and the righteousness of God. Romans 1:16-17 says:
For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek. For in it the righteousness of God is revealed from faith to faith; as it is written, “But the righteous man shall live by faith.”
Paul goes on, in the next ten chapters or so, to outline the foundational doctrines of Christianity; he finishes his letter (the book) with some practical advice about how to live out those principles on a daily basis. Chapter twelve begins with the word "so," indicating that all that came before is one thing (teaching) and what follows is another (practice). This is the foundation of all learning and growing in every area of life: first learn the principles and then apply them.
We are imperfect learners and appliers, but we have the book of Romans from which to continue learning and applying. It is an essential book of the New Testament.