According to my copy of the New Oxford Annotated Bible, which is a standard academic study Bible (something doesn’t get put in it unless it has significant backing), Matthew was written probably around 80, Mark prior to 66, 85 (give or take 5 to 10 years either way) for Luke, and around 90 for John. I have had one professor argue quite convincingly for a much earlier date for John, and another for Matthew.
What is also important is the number of independent witnesses. If you take each of the Gospels to be written by the man for whom they are named (a tradition which arose later, but which also has little to no evidence backing it up), the Gospels present four independent witnesses. Again, this is unlikely.
Matthew, Mark, and Luke are called the Synoptics, as they are closely related and are probably interdependent, apart from John. That means, with the standard scholarly position, there are two idependent witnesses to the life, teachings, and death of Jesus. Paul presents a third (he was likely present for some of Jesus’ preaching and his death, due to where Paul was known to be at the time of these events). The more independent witnesses to an event, the better attested it is.
I would reccomend N.T. Wright’s The Resurrection of the Son of God, which details the arguments for the reliability of the Resurrection narrative, many of which apply to the whole of the Gospel narratives. It is a wholly masterful cinder block of a book.
Also, keep in mind that the Gospels are ancient works; the ancient peoples wrote history and biography different from us today, with different goals and preoccupations. It is a mistake to assume the Gospels are written in the same way a journalist would write today, for example. In fact, the Gospels (especially John and Matthew) have much the character of extended sermons, written for an explicit theological point.
Unfortunately, arguing that the Gospels are accurate because the Church declares them to be so, and we believe the Church because of events in the first century is circular reasoning. Fortunately, however, we have enough data to support the reliability of at least the basic plotline of the Gospels, if not the total factuality of each word.
The most important event of them all is the Resurrection of Jesus. After all, Paul says, “If Christ has not been raised, your faith is futile and you are still in your sins. Then those also who have fallen asleep in Christ have perished. If for this life only we have hoped in Christ, we are of all men most to be pitied” (1 Cor. 12:17-19 RSV). We have more than enough evidence for this particular event. Again, see the book mentioned above.