Most people are so familiar with red letter Bibles that we assume they have always been around. Actually the first red letter New Testament was published in 1899 and was included in a full Bible in 1900.
This common trait of most modern Bibles originated from one man - Louis Klopsch could rightly be called the inventor of the red letter Bible. Klopsch's idea of printing the words of Jesus in red originated in Luke 22:20, which says: This cup is the new testament in my blood, which I shed for you. This inspired Klopsch to ask his mentor what he thought of printing the words spoken by Jesus in red, to which he replied, "It could do no harm and it most certainly could do much good."
So with that little history lesson :) We must realize that the "red letters" are no more inspired, no more authoritive, no more the Word of God than any other passages in Scripture. It is easy to look at what Jesus said, and hold it in a higher regard than the rest of the Bible. But, ALL scripture is God breathed! When Jesus preached the "Sermon on the Mount" the message is equally infallible & authoritive as when we read the letters from Paul to the churches (as an example). We should read the Word under the submission to what it says regardless of who God is using to speak in His Word.
That being said, there is currently a Bible that has the entire Bible red lettered (the Old Testament has the words spoken by God in red). For anyone who could benefit from this as a study tool - here is the link.