There are solid reasons for trusting in today's list of New Testament books. The church accepted the New Testament books almost as soon as they were written. Their authors were associates of Jesus or his immediate followers, men to whom Jesus had entrusted the leadership of the early church.
The Gospel writers Matthew and John were some of Jesus' closest followers. Mark and Luke were companions of the apostles, having access to the apostles' account of Jesus' life.
The other New Testament authors had immediate access to Jesus as well: James and Jude were half-brothers of Jesus who initially did not believe in him. Peter was one of the 12 apostles. Paul started out as a hater of Christianity, but he became an apostle after he had a vision of Christ. He was also in communication with the other apostles.
The content of the New Testament books lined up with what thousands of eyewitnesses had seen for themselves.
When other books were written many years later (e.g. the Gospel of Judas, written by the Gnostic sect around 130-170 A.D., long after the real Judas' death), it wasn't difficult for the church to spot them as forgeries.
The Gospel of Thomas, written around 140 A.D., is another example of a counterfeit writing erroneously bearing an apostles' name. These and other Gnostic gospels conflicted with the known teachings of Jesus and the Old Testament, and often contained numerous historical and geographical errors.
In A.D. 367, Athanasius formally listed the 27 New Testament books (the same list that we have today). Soon after, Jerome and Augustine circulated this same list.
These lists, however, were not necessary for the majority of Christians because by and large the majority of leaders and congregations had recognized and used the same list of books from the time they were first written and circulated.
For example:
Clement (30-100 A.D.) wrote an epistle to the Corinthian Church around 97 A.D. He reminded them to heed the epistle that Paul had written to them years before. Clement had labored with Paul (Philippians 4:3). He quoted from the following New Testament books: Luke, Acts, Romans, 1 Corinthians, Ephesians, Titus, 1 and 2 Peter, Hebrews, and James.
The apostolic fathers Ignatius (30-107 A.D.), Polycarp (65-155 A.D.), and Papias (70-155 A.D.) cite verses from every New Testament book except 2 and 3 John. They thereby authenticated nearly the entire New Testament. Both Ignatius and Polycarp were disciples of the apostle John.
Justin Martyr, (110-165 A.D.), cited verses from the following 13 books of the New Testament: Matthew, Mark, Luke, John, Acts, Romans, 1 Corinthians, Galatians, 2 Thessalonians, Hebrews, 1 and 2 Peter, and Revelation.
Irenaeus, (120-202 A.D.), wrote a five volume work Against Heresies in which, He quoted from every book of the New Testament but 3 John. He quoted from the New Testament books over 1,200 times.
As the church grew beyond the Greek-speaking lands and needed to translate the Scriptures into foreign languages, and as splinter sects continued to pop up with their own competing unofficial holy books (often written by themselves) , it became more important to provide them with a definitive list of what the correct books were which is why Athanasias in 367 AD confirmed which books had historicaly always been accepted by Christians as scripture.