The missing books you refer to in the KJV are most likely the apocryphal books which are generally not found in any Protestant translation (NASB, NAS, NIV, RSV, etc.). The Protestant church generally does not believe these books are inspired and therefore canonical, that is authoritative and deserving to be a part of the Bible as the Word of God. The books in question are considered apocryphal in most Protestant churches, but are accepted as canonical in the Roman Catholic Church, the Eastern Orthodox Church, and the Armenian and the Ethiopian Oriental Orthodox Churches.
There are 14 of these books found in the Septuagint and included in the Vulgate but considered uncanonical by Protestants because they are not part of the Hebrew Scriptures. The Roman Catholic canon accepts 11 of these books and includes them in the Douay Bible.
The following explanation from the Encarta® 98 Desk Encyclopedia © 1996-97 Microsoft Corporation may help.
Apocrypha, term coined by the 5th-century biblical scholar Saint Jerome for the biblical books received by the church of his time as part of the Greek version of the Old Testament (see Septuagint), but not included in the Hebrew Bible.
Derived from the period 300 BC to New Testament times, the books of the Apocrypha included Judith, the Wisdom of Solomon, Tobit, Sirach (Ecclesiasticus), Baruch, and the two books of Maccabees. Also generally included with the Apocrypha are the two books of Esdras, additions to the Book of Esther (Esther 10:4-10), additions to the Book of Daniel (Daniel 3:24-90;13;14), and the Prayer of Manasseh.
Roman Catholic and Orthodox Christians include all the Apocrypha in the biblical canon, except for the two books of Esdras and the Prayer of Manasseh. They generally refer to the Protestant Apocrypha as deuterocanonical books, and reserve the term Apocrypha for those books entirely outside the biblical canon, which Protestants call the Pseudepigrapha.
The Reasons the Protestant Church excludes them is as follows:
1. The early church fathers only accepted the thirty-nine books of the Old Testament. The only exception was Augustine (A. D. 400) who included the books of the Apocrypha (those “extra” books that some Bibles include between the books of the Old and New Testaments). However, he did acknowledge that they were not fully authoritative.
2. The books of the Apocrypha were not officially recognized as part of the canon until the Council of Trent (A.D. 1546) and then only by the Roman Catholic church.
3. There are some 250 quotes from Old Testament books in the New Testament by the writers of the New Testament, but none from the Apocrypha. All Old Testament books are quoted except Esther, Ecclesiastes, and the Song of Solomon.
4. In Luke 11:51, the Lord said something definitive about the extent of the canon of the Old Testament which He accepted. In condemning the leaders of the Jewish people for killing God’s messengers throughout their history, He charged them of being guilty of shedding the blood of all the righteous from Abel to Zechariah. Now the murder of Abel is recorded in Genesis 4, and the murder of Zechariah in 2 Chronicles 24 which in the arrangement of the Hebrew canon was the last book in order (as Malachi is in our arrangement). So the Lord was saying, “From the first to the last murder recorded in the Old Testament.” Now, of course, there were other murders of God’s messengers recorded in the Apocrypha, but the Lord does not include them. Evidently He did not consider the books of the Apocrypha to be of equal authority with the books from Genesis to 2 Chronicles.
Beyond the Apocrypha, there were many other books that were considered false and were called the pseudepigrapha. These were spurious writings, especially writings falsely attributed to biblical characters or times. They included a number of texts written between 200 B.C. and A.D. 200 and spuriously ascribed to various prophets and kings of the Hebrew Scriptures.
Jewish and Christian writings that began to appear about 200 BC and continued to be written well into Christian times; they were attributed to great religious figures and authorities of the past. Pseudepigrapha were composed in Hebrew, Aramaic, and Greek, and they include apocalyptic writings, legendary histories, psalms, and wisdom literature. In most cases, Pseudepigrapha are modeled on canonical books of a particular genre. Although Pseudepigrapha, in the sense of pseudonymous works, are included in the canon of the Old Testament (see Bible), Protestants and Jews customarily use the term Pseudepigrapha to describe what Roman Catholics would term Apocrypha— late Jewish writings that all scholars consider extracanonical (Encarta® 98 Desk Encyclopedia © & 1996-97 Microsoft Corporation).
Other than these, I know of no other books that could be involved here. Historically, the books of our present-day Bible, as found in the KJV and NASB, etc., are the only ones that the Protestant church has recognized as inspired of God and thus canonical. For more information on the issue of canonicity, see the study, Bibliology: The Doctrine of the Written Word on our web site as well as other studies on canonicity.