When were the Gospels written and how can we find out when they and other New Testament documents were made?
Let’s look at some writers in the late 1st century and 2nd century and also at the events the New Testament writers mentioned and didn’t mention.
This information has been set out in a time line from about A.D. 30 (Jesus′ death and resurrection) to after A.D. 110.
Irenaeus, who lived from about AD 130 to 202, commented that (the Apostle) John wrote his Gospel and his letters (1 John, 2 John and 3 John) after the three Gospels were written (Matthew, Mark and Luke). 
– A.D.110 –
Polycarp, who lived about AD 69 to 155, was a disciple of the apostle John and who taught Irenaeus in one of his letters written about A.D. 110 to the Philippians, refers to the: 4 Gospels, the book of Acts and 13 other New Testament books.  Both Irenaeus and Tertullian record that Polycarp had been a disciple of John, one of Jesus’ disciples. 
– A.D.108 –
Ignatius, who died AD 110, in 7 letters around A.D. 108, refers to the: 4 Gospels, Acts and 19 other New Testament books. 
Clement of Alexandria, who lived about AD 150 to 215, (recorded by Eusebius who lived about AD 260 to 340) said that John wrote to supplement the writings of the other Gospels. 
It is thought that John′s Gospel was written in the A.D. 90′s. But this is not proved, and it could have be written earlier than that.
The Book of Revelation probably written A.D. 96
– A.D.96 –
Clement, writing from Rome in about A.D. 96 refers to Matthew, Mark, and Luke, and 8 other New Testament books. 
Conclusion so far: At least 25 of the 27 books of the New Testament were in circulation by about the year A.D.100.
The 3 letters of John probably written A.D. 90
The Book of Hebrews was written earlier than A.D. 70
– A.D.70 –
The book of Acts is a history of the early church and it has got a lot of historical detail. So it is logical to be able to put a date on this book. Acts does not record the monumental fall of Jerusalem in A.D. 70, when the Romans literally flattened it. The Temple was also demolished, surely this event would have been recorded if Acts had been written after A.D. 70.
Jude′s letter probably written A.D. 66
Peter′s second letter probably written A.D. 66
– A.D.65 –
Acts does not mention Nero′s massive persecution on Christians in about A.D. 65. To omit this seems unlikely, because other persecutions were described within Acts. So Acts must have been written before this date.
Second letter to Timothy may possibly have been written A.D. 65
– A.D.64 –
Acts stops short of the result of Paul′s arrest and appeal to Caesar (Acts 28:17-19 and 30-31). Probably this was due to the outcome not being known at the time Acts was written. It is thought that Paul was martyred in A.D. 64, so Acts must have been written before that. 
Letter to the Colossians probably written A.D. 64
Letter to the Ephesians probably written A.D. 64
Letter to the Philippians may possibly have been written A.D. 64
Letter to Philemon probably written A.D. 64
– A.D.61 –
Acts does not mention the killing of James in A.D. 61 and Peter in A.D. 65, whereas Stephen′s death is. 
…the material we find present in Acts fits very well with it being written in the early 60′s A.D.”
Douglas Groothuis 
Book of Acts probably written A.D. 60
The Gospel of Luke was written before Acts:
In my former book*, Theophilus, I wrote about all that Jesus began to do and to teach until the day he was taken up to heaven, after giving instructions through the Holy Spirit to the apostles he had chosen.
After his suffering, he presented himself to them and gave many convincing proofs that he was alive. He appeared to them over a period of forty days and spoke about the kingdom of God.”
Acts 1:1-3 * this ‘former book’ is known as the Gospel of Luke.
In Luke Jesus prophesies the fall of Jerusalem because they rejected the Messiah (Luke 13:34-35). It would be unimaginable for Luke not to mention such a fulfilment of prophecy if he were writing after A.D. 70 (which was when Jerusalem was destroyed by the Romans). Therefore Luke′s Gospel must have been before A.D. 70.
The modern view is that Luke seems to rely on the ‘eye witness accounts’ of Mark and Matthew as sources of information (Luke 1:1-4) although this cannot be proved.
Most modern scholars believe that Mark was written before Matthew and Luke, because it seems the latter two quite often refer to material in Mark, using it as one of their primary sources.’
 This cannot be proved either.
The dating of Acts and the Gospels is hotly contested, and absolute certainty is unavailable.’
E. F. Bruce dates: Mark at around A.D. 64 or 65, Luke shortly before 70, and Matthew shortly after 70, 
Letter to the Romans probably written A.D. 60
Second letter to the Corinthians probably written A.D. 60
Letter to the Galations probably written A.D. 60
Peter′s first letter probably written A.D. 60
First letter to the Corinthians probably written A.D. 59
First and second letters to the Thessalonians probably written A.D. 54
James′ letter probably written a lot earlier.
William F. Albright, the distinguished archaeologist and biblical scholar, affirmed that:
every book of the New Testament was written by a baptised Jew between the forties and the eighties of the first century A.D.
(very probably sometime between about A.D. 50 and 75).’ 
– A.D.30 –
Jesus′ death and resurrection was about A.D. 30.
Key to reference sources:
 Paul Barnett, Is the New Testament History? (Ann Arbor, MI: Servant Publications, 1986), p38-39
 Lewis Foster, Introduction: Acts of the Apostles, in The NIV Study Bible, Kenneth L. Barker, ed. (Grand Rapids, MI: Zondervan, 1985) p1641
 Douglas Groothuis Jesus In An Age Of Controversy (Kingsway Publications, 1998 ISBN 0 85476 729 0) p44
 Douglas Groothuis Jesus In An Age Of Controversy (Kingsway Publications, 1998 ISBN 0 85476 729 0) p42
 Douglas Groothuis Jesus In An Age Of Controversy (Kingsway Publications, 1998 ISBN 0 85476 729 0) p45
 Toward a More Conservative Faith: Interview with William F. Albright, Christianity Today, January 18, 1963, p3.
 F.F. Bruce, The New Testament Documents: Are they Reliable? 6th ed, (Grand Rapids, MI: Eerdmans Publishers, 1987), p12.
 Irenaeus, Against Heresies, 3.1.1.
 Eusebius, Ecclesiastical History, 6.14.7.
 Wikipedia.org (opens in a new page)
Picture of the Temple being plundered on the Titus arch in Rome, by David Alexander, (The Lion Handbook to the Bible), with thanks.
Scroll image: thanks to GSP 100,000 Clipart CD