What happens in a culture of this kind, is that certain means of expression become standardized in the process of story telling. In a literary culture such as our own, whenever we do communicate a story orally rather than in written form, we tend to tell the story a little differently every time we tell it in order to make it more interesting. This is taboo in an oral culture. You grow up knowing that the only way your children are going to understand their past is by hearing from you the exact story in the exact wording in which it was conveyed to you. It is difficult for us to imagine such a culture, but such cultures have been common since the beginning of human history. The culture into which Jesus was born did use literary documents, but it was primarily an oral-tradition-based culture.
The individuals in such a culture are in the position of being dependent on their memory. We are not; since information is usually recorded, we know that if we forget something we can re-obtain our knowledge by going back to the records. Members of an oral-tradition-based society have no such assurance. Since their memories are exercised to a much greater degree than ours, our memory capacities are atrophied by comparison.
There is plenty of evidence that members of societies based on oral tradition were capable of memorizing extraordinary amounts of information. Moreover, the ancient Jews were experts in maintaining oral tradition, and had extraordinary memory capacities, many of them memorizing the Pentateuch, and rabbis memorizing the entire Old Testament. They eventually wrote the Mishnah about AD 200, the Jerusalem Talmud between AD 350 and 400, and the Babylonian Talmud about AD 500. These documents record volumes of oral tradition, some of which dated back centuries before Christ. Because of the reliability of their oral tradition the Jews considered it more reliable than written records.
With this in mind, let me make several points (some of which I've mentioned before).
1) Since the gospel authors translated Jesus’ sayings from Aramaic into Greek (or at least most of them -- he may have spoken Greek and Hebrew as well), when we translate them back into Aramaic, we find that most of them have a clear mnemonic form. In other words, Jesus taught in ways that could be memorized easily. He used contrasts, parallels, parables, even poetry to get the message across. For example, Jesus’ statement that the Pharisees and teachers of the law "strain out a gnat and swallow a camel" (Matthew 23:24) makes more sense when translated back into Aramaic, since the words "gnat" and "camel" are almost identical (galma and glama). In Greek and English, it’s a metaphor. In Aramaic, it’s also a pun. Whether Jesus’ status as a punster conflicts with his claim to deity is something I leave to the reader.
2) The attitude of Jesus’ disciples towards him was like that of students to a rabbi. This is significant since the teachings of rabbis was frequently considered sacred tradition which was to be memorized.
3) It’s at least probable that Jesus would have repeated his most effective sayings many times.
4) Even the longest discourses of Jesus in the gospels only take a few minutes to read through. But he taught for hours and days at a time (Mark 8:1-3).
5) First century Judaism was not a myth-friendly environment. Any claim of legendary development of the gospels or of an "inventive early Christian community" completely ignores the culture, society, and belief system it supposedly happened in.
6) The sayings of Jesus and the events in the gospels were not only discussed daily among friendly eyewitnesses, who wanted to preserve Jesus’ original sayings and the events of his life, but was preached daily to hostile eyewitnesses who had every motive to point out discrepancies and errors.
7) The gospels aren’t very long. Each one records a few dozen pages of information about a three year period in the recent past. This would be equivalent to someone in their 40s or 50s writing a few dozen pages about their experiences in high school. That’s not a problem for those of us who don’t live in an oral-tradition-based culture.
8) The NT is remarkably consistent. As Kreeft and Tacelli write in Handbook of Christian Apologetics, "The only inconsistencies are in chronology (only Luke’s gospel claims to be in order) and accidentals like numbers (e.g., did the women see one angel or two at the empty tomb?)." But, whatever inconsistencies there may be in some of the details, the gospels all agree on the central events. Thus, to use the inconsistencies to call the main events into question is as irrational as saying that since the eyewitnesses to a hit-and-run accident disagree on the color of the car that drove off, no car accident took place. Moreover, many of the inconsistencies can be resolved. The first harmonization of the four gospels, the Diatessaron, was written circa AD 160-175 by Tatian. Many others have been written since.
9) On the heels of this, since there are four gospels, "a lot of cross-checking is possible. By a textual trigonometry or triangulation, we can fix the facts with far greater assurance here than with any other ancient personage or series of events" (Kreeft and Tacelli).
10) The gospels weren’t the first records written. The letters of the apostle Paul were being written by AD 50 or earlier. These are all consistent with the gospels’ portrait of Jesus. Even those who are fanatically opposed to Christianity are forced to concede this. Joseph McCabe, for example, writes in The Myth of the Resurrection and Other Essays:
God, a purely spiritual being, takes human shape in Jesus, and sheds his blood on a cross, is buried, and then, in human shape, comes to life again. I do not see how anybody not obsessed by a theory can fail to recognize that, less than ten years after the alleged crucifixion of Jesus, Paul fully accepted that part of his story. "Being found in fashion as a man, he humbled himself, and became obedient unto death, even to death on the cross." With infinite variations of expression, that formula is found in every Epistle, and it is Paul’s fundamental belief about Jesus. ... No one has ever suggested that Paul had any doubt about the divinity of Jesus. ... there are a hundred passages in which he says that Jesus was crucified, and by the Jews, and there are a thousand references to his physical resurrection.
11) Paul, and other NT authors, quote creeds and hymns which preceded their writings. Most scholars date them to between AD 33 and 48. They are distinct from the surrounding material in five significant ways: (a) they are frequently referred to as pre-existent material of which the original audiences were already aware; (b) they are uncharacteristic of the general style in which the authors in question wrote; (c) they use language and phrases which were completely out of use by the time the NT began to be written; (d) like Jesus’ sayings, they translate back into Aramaic easily; and (e) as Moreland writes in Scaling the Secular City, "they show features of Hebrew poetry and thought-forms. This means that they came into existence while the church was heavily Jewish and that they became standard, recognized creeds and hymns well before their incorporation into Paul’s letters." For example, 1 Corinthians 15:3-8 is dated by most scholars to AD 38 at the latest. This creed cites that Jesus died for our sins, was buried, and came back to life a few days later, appearing to individuals and groups of up to 500 people. Paul adds that most of the 500 who saw Jesus at one time were still alive to be questioned. Since Jesus was crucified in AD 30 or 33, that gives us eight years at most to explain how such a belief could have arisen, and most scholars would put it at five years or less. Similarly, Philippians 2:5-11 contains a creed which refers to Jesus as being "in very nature God", and Colossians 1:15-18 contains a creed which refers to Jesus as the "image of the invisible God" and the Creator and Sustainer of the universe.
12) Early source material used by Mark in his gospel has been dated by most scholars to the AD 30s as well. Many scholars also speculate that a collection of Jesus’ sayings, dubbed "Q", was written in the 40s.
13) There is no remnant of any story about Jesus other than the one recorded in the NT. As Craig writes in Reasonable Faith,
The letters of Barnabus and Clement refer to Jesus’ miracles and resurrection. Polycarp mentions the resurrection of Christ, and Irenaeus relates that he had heard Polycarp tell of Jesus’ miracles. Ignatius speaks of the resurrection. Quadratus reports that persons were still living who had been healed by Jesus. Justin Martyr mentions the miracles of Christ. No relic of a nonmiraculous story exists. That the original story should be lost and replaced by another goes beyond any known example of corruption of even oral tradition, not to speak of the experience of written transmissions. These facts show that the story in the Gospels was in substance the same story that Christians had at the beginning. (emphasis mine)
Even if the first records about Jesus’ life weren’t written until the end of the first century by unknown authors, they would still be considered generally reliable by common historical standards. Of course, there are scholars who claim that the NT documents are not historically reliable. The problem is that they start their investigations by presupposing that supernatural events have never occurred. As such, any evidence which leads to the conclusion that they have occurred can be justifiably dismissed. Thus, their arguments are completely circular: they assume that miracles cannot happen, they examine the NT documents, and conclude that the miracles recorded in it didn’t happen. In other words, their conclusions about the historical validity of the NT are not a product of the evidence but of their presuppositions. They would have reached the same conclusion regardless, since it’s simply a re-statement of their starting point. But if we begin by allowing the possibility of miracles, we come to significantly different conclusions.
Update (15 Feb): See also part 1, part 2, part 3, and part 5.