Joshua Foer, in his book on memory, Moonwalking with Einstein, observed this about adding versification to the Bible:
For the first time, a reader could refer to the Bible without having previously memorized it. One could find a passage without knowing it by heart or reading the text all the way through. (144)
This observation is quite important because when we notice obvious quotations of the Old Testament in the New Testament, it is likely that this rhetorical device was meant to bring a range of emotions, concepts, and themes to mind that were exemplified by the context of the passage quoted. It is certainly possible to over-read things when we make this realization. The opposite danger is more readily possible though. If we assume that ancient readers thought of the Bible in terms of discrete versified units, then we are contradicting a fact about human memory that has been documented by modern science and thousands of years of observations by practitioners of memorization. So, when you notice a quote of the Old Testament in your New Testament, go read the context or the whole book. You’ll get a better picture of what the New Testament author is saying.