Cameron's post presents a view of the order and dating of the four Gospels which substantially agrees with the beliefs of the early church about these matters. However, the presentation may not be of much value in convincing the skeptic, as it is full of conjecture. There is nothing wrong with such conjecture, and I have many conjectures of my own, but such arguments may not impress the man who is looking for the facts.
In our day, most New Testament scholars believe in the "priority of Mark"--meaning they believe that Mark's Gospel was written before the others and served as one of at least two sources for the material in Mathew and Luke. The other alleged source is a document that is entirely hypothetical. No one has ever found it and it may never have existed. Scholars have dubbed this phantom document "Q" (the initial letter of the German word for "source").
According to most scholars, Mark's Gospel contributed most of the narrative material for Matthew and Luke, whereas "Q" supplied much or most of the sayings of Jesus, few of which are found in Mark. John's Gospel is recognized as an entirely independant production, not related to the other three Gospels.
I disagree with these scholars, primarily because their premises seem flawed (why would Matthew, an eye-witness, for example, have to depend upon "sources" other than his memory?), and also because of the beliefs of the early church fathers from earliest times.
The earliest church fathers believed in the priority of Matthew, not Mark. In agreement with what Cameron said above, the fathers taught that Matthew first wrote a catalogue of the sayings of Jesus in Aramaic (the language spoken by Christ and the apostles). This Aramaic document might have been translated directly into Greek to become our Gospel of Matthew, or the present book may have been an expansion upon the original work.
Mark was indeed Peter's "interpreter" (according to Papias), and seems to have written in his Gospel only what he heard from Peter. Mark was also an inhabitant of Jerusalem during the lifetime of Christ, and may have witnessed some of the events he records with his own eyes as well, but the real authority behind his Gospel is Peter.
Luke is well-known to us as Paul's companion, and he was probably not an eye-witness of any of the events recorded in his Gospel. However, he knew the apostles personally, and interviewed people whom he describes as eye-witnesses (Luke 1:2), which makes his Gospel pretty authoritative in my judgment.
The author of the Fourth Gospel was "the beloved disciple" (John 21:20-24), who is credibly identified as John. This man was one of Jesus' "inner circle" and witnessed most of the things Jesus said and did in the years of His public ministry. He specifically affirms that he was an eye-witness of the crucifixion (John 19;35). His material does not overlap that of the three synoptic Gospels much. The reason appears to be that John wrote later than the others, and saw no need to duplicate their material. In his old age, he was the last surviving witness of many things that had not been recorded in the other Gospels, and so he left a record of his memoirs to supplement the existing recorded history of Christ.
The strongest reason to accept the above summary is that it was passed down to us by men living at the end of the first century, when the trail of the Gospels' literary history had not yet gone cold. Papias, our main source for this information, lived at the end of the first century, and may have known John. Certainly his testimony carries more weight than do the speculations of critics living 2000 years removed from the appearance of these documents.
As for the dates of the Gospels' appearance, the fathers have not left us exact information. However, this much can be reasonably deduced:
1. Luke wrote Acts, apparently, when Paul was still in prison, awaiting trial before Nero. Paul had been in Rome under house arrest already for two years at the time of Luke's writing the Book of Acts (Acts 28:30). Since Paul arrived in Rome in AD 60, this would mean that Acts was written in AD 62.
2. We know that the book of Luke was written before the book of Acts (Acts 1:1), so Luke must have been written no later than, say, 60 or 61 AD.
3. Luke was not the first to write a Gospel. He knew of "many" who had done so previous to him (Luke 1:1). It is a fair inference that Matthew and Mark were among those "many," since all scholars either believe in the priority either of Matthew or of Mark. This suggests that these two Gospels were written prior to about AD 60...perhaps considerably earlier.
4. Some scholars have believed that Mark's Gospel appeared as early as AD 50, which may or may not be the case, but Papias suggests that Matthew's Aramaic version existed earlier still than all the other Gospels. In any case, the evidence suggests that all three synoptic Gospels were written no later than AD 60 (see points 1 through 3, above), which was only 30 years after the events that they describe, and well within the lifetimes of hundreds of people who actually saw Jesus, and who could have refuted the Gospel accounts, if they were very inaccurate.
5. Since John wrote the Fourth Gospel, it is clear that it must have appeared in the first century as well, though possibly near the end of John's life, in the last decade of the first century.
The above analysis is derived from the best internal and external evidence available in the early centuries of the church, and there is nothing about these conclusions that is inherently unlikely, or that can be disproven by modern scholarship.
F.F. Bruce has rightly observed that those who discount the historical reliability of the Gospels are not historians, but, rather, liberal theologians. The historical accuracy of the Gospels is well-attested by the normal procedures of historical research. The liberal theologians have an agenda that makes them wish to reject the recorded actions and claims of Jesus Christ. The most effective way to do this is to disregard the records of His life that have come down to us. However, this they cannot do by any appeal to historical data.
For more on this subject, see my answer to Melissa at
http://www.wvss.com/forumc/viewtopic.php?t=84