What is the "verbal plenary" view of the inspiration of Scripture and to what texts is it considered to apply? What hermeneutical approaches hold this view and how does it affect the way they prioritize different manuscripts in their pursuit of the meaning of a given passage?
Verbal Plenary Inspiration means that the very words of the original manuscripts were directly inspired by God, although he did not change the author's intelligence or understanding while doing so. Meaning, that God choose, inspired and sovereignly guided the biblical authors who were equipped by Him to write the very words of scripture. This is the foundation of the evangelical view of the inerrancy of scripture.
This should only apply to the canonical books within the tradition in which the doctrine is accepted. As a Protestant I believe this applies only to the canonical books of the Protestant Bible.
This is a view mainly held by Protestants, so I would offer this as a general statement: if you hear someone espouse this view then they are probably referring to the Protestant Bible. If I am incorrect I would gladly take correction, but I do not think my Catholic and Eastern Orthodox brothers would agree with this doctrine or apply it to their canon.
From Wikipedia as an outside source:
Note: Although I think there is some evident bias against this doctrine in the Wikipedia entry it does represent a valid, secular look at the idea.