Ancient historians often put long speeches into the mouths of historical figures. Generally, we take the gist of these speeches as informative in an accurate way, but of course the entire speech was not recorded with a tape recorder. Short sayings, however, are often taken verbatim. I don't think anyone doubts Suetonius' assertion that Augustus liked to say "make haste slowly" or Dio Cassius' claim that the Emperor said, "I would rather be Herod's pig than his son." Such quotable sound bytes are memorable for obvious reasons, and thus inherently trustable. If the so-called 'telephone game' had affected those statements much, they would never have been so notable. Besides, both lines befit the people involved and line up with the facts.
Now what about the Gospels? Jesus makes long speeches in all of them. Luke's version of the "sermon on the mount" is much abbriged from Matthew's. Yet within all Jesus' speeches are a great many "quotable soundbytes". Also, the content was usually much more dramatic and impactful than legal arguments or political appeals. We shouldn't be too quick to doubt them as being accurate to a fairly high degree, if not absolutely verbatim.
In addition, it is not necessary to believe the first written versions came decades later (as scholars generally assume). As I have argued here repeatedly, the Jewish culture was a highly literary one, if not a highly literate one. Writings and readings were an enormous part of the Jewish identity and daily experience. Since Jesus' followers undoubtedly considered Moses and the Prophets to have been traveling writers, as well as speakers, it is highly plausible to suppose the disciples would have worked as a group to make sure at least one educated man among themselves was updating a written account, along the way. (As should be well known by now, I believe that man was probably Matthew.)
With all of that, I do not think christians need to (or should) believe that every "red letter" word in the Gospels was spoken by the Lord precisely as recorded. Honestly, I stand with those who say that if the ancients themselves didn't expect verbatim accounts, we should accept that and understand the historical limitations of ancient speech recording.
And now with that balancing remark, I certainly believe christians should take all the "red letter" words as if they were spoken verbaitm. On the other hand, how do we determine what to take from Jesus' speeches for the purposes of historical reconstruction? How much can (or should) we consider as verbaitm? I gonna take a stab now, even though I know I'll keep percolating on this for a long time to come... [Update: I am essentially done percolating on John. The Synoptics, however, are my focus in this post.]
Ironically, those who say the Gospel writers added "theological" content of their own may actually give us a way to believe Jesus' speeches have MORE historical reliability... that is, IF those "theological" insertions were actually, honest-to-goodness, divine revelations of God. But I'm not saying the writers were given dictation as if God was the tape recorder during the speeches. I'm saying that if the writings are truly inspired, then we should confidently consider them virtually accurate.
I guess what I'm basically saying is that "close counts" in horseshoes and holy scripture. ;-)