Rebuilding the Foundations
Protestants tend to call the seven extra books that are in the Roman Catholic Old Testament "The Apocrypha." "Apocrypha" means "hidden" or "secret," and is not really the right word for those books. The right word is "deuterocanonicals," which means "a second canon."
It's not just the Roman Catholics who have deuterocanonical books. I counted the books in my Orthodox Study Bible, and there are ten extra in it. Other branches of eastern Orthodoxy have even different canons. The Ethiopian Orthodox Church even includes the Book of Enoch in their canon. The Assyrian Church of the East (Nestorian) ends their New Testament at 1 John, leaving out 2 & 3 John, Jude, and Revelation.
One other large difference between the various branches of Christianity—indeed between western and eastern Christianity—is the text from which the Old Testament is translated. Catholics and Protestants translate their Old Testaments from the Hebrew Masoretic text, while all eastern churches (mostly Orthodox) use the Septuagint, a Greek translation of the Hebrew made a century or two before Jesus' birth.
You might want to follow that link for more information on the Septuagint, which was usually the translation of choice for the apostles when they wrote to Greek churches and traveled in the Greek-speaking Roman empire. For now, though, it is off topic on the Deuterocanonicals except to mention that it includes them, and even more of them than the Roman Catholics do.
Who gets to determine what is the canon, the actual accepted books of the Bible?
Apparently, each individual church gets to determine, though over time they colluded with other churches into large organizations such as the Roman Catholic Church and the Greek Orthodox.
Despite all the rumors, no council with any authority ever ordered a canon that was binding on all churches until the Council of Trent in the sixteenth century. Of course, the Council of Trent is only binding on Roman Catholic Churches, though their official doctrine is that their decrees are binding on all Christians in the world (Catholic Catechism. Par. 882).
That's right, there was no official, authoritative proclamation of which books are in the Bible until the sixteenth century!
Many of us have heard that the Council of Nicea determined the books of the Bible in AD 325. That's not true. They never even discussed the books of the Bible.
I have been told before that the Synod of Hippo set the canon for all the churches in AD 393. If so, Augustine, the bishop of Hippo beginning in 396, didn't know about it! Just a few years later, in 412, he wrote:
Accordingly, among the canonical Scriptures he will judge according to the following standard: to prefer those that are received by all the catholic churches to those which some do not receive. Among those which are not received by all, he will prefer such as have the sanction of the greater number and those of greater authority to such as are held by the smaller number and those of less authority.
If, however, he shall find that some books are held by the greater number of churches, and others by the churches of greater authority (though this is not a very likely thing to happen), I think that in such a case the authority on the two sides is to be looked upon as equal. (On Christian Doctrine II:8:12.)
The various churches had a canon that was very similar with only small differences over the same questionable books. (You can find all the early canon list, dating back to the second century, on Christian History for Everyman.) Nonetheless, there were enough differences for Augustine to refer to them in AD 412.
Oddly enough, it could be said that Jerome set the Protestant canon all by himself! It was the popularity of Jerome's Latin Vulgate in the west, which contained his disparaging remarks about the seven deuterocanonical books, that put them in question. They were never in question in the eastern churches, carrying down through time in the Greek Septuagint.
The Catholic Encyclopedia has a very interesting article on the canon that explains all this. You would probably enjoy scrolling down to the section titled "The canon of the Old Testament from the middle of the fifth to the close of the seventh century" and reading from there.
You may be crying out, "What happened? I thought there was a good, set, agreed upon number of books in the Bible that everyone knew were inspired by God!" There are a few things it is important to remember: