The original intention of red-letter Bibles seems to have been to aid in interpretation. According to Crossway, the publisher of the English Standard Version:
In the first red-letter Bible, the words “universally accepted as the utterances of our Lord and Saviour” were printed in red. So were Old Testament passages that Jesus quoted or that were directly related to incidents to which he referred (with the relevant cross reference also printed in red). Old Testament verses containing prophetic references to Christ were identified with red stars.
Lous Klopsch, who invented the concept, described its use thusly:
Here the actual words, quotations, references and allusions of Christ, not separated from their context, nor in a fragmentary or disconnected form, but in their own proper place, as an integral part of the Sacred Record, stand out vividly conspicuous in the distinction of color. The plan also possesses the advantage of showing how frequently and how extensively, on the Authority of Christ himself, the authenticity of the Old Testament is confirmed, thus greatly facilitating comparison and verification, and enabling the student to trace the connection between the Old and the New, link by link, passage by passage.— “Explanatory Note,” in The Holy Bible: Red Letter Edition (New York: Christian Herald, 1901)
This doesn't seem to far from the way some people mark up [PDF] their Bibles for inductive studies. Only it's the publisher and not the reader who has done the analysis.
In my reading and studying of the Bible, there is almost no reason to seek out or use a "red-letter" edition. Every once in a while, I find Jesus' words in an unexpected place:
In all things I have shown you that by working hard in this way we must help the weak and remember the words of the Lord Jesus, how he himself said, ‘It is more blessed to give than to receive.’”—Acts 20:35 (ESV)
But for the most part, I find the red-lettering disruptive.
My guess is that part of the appeal of such editions is that they show reverence for Our Lord's words. It's a nice idea, but it doesn't seem to me to make any difference. God is more likely to be honored by us reading His Word in toto than by us owning a Bible with some of His words in red. (The Old Testament never gets this treatment anymore.) If the highlighting makes the Bible harder to read, I don't see how we gain anything.