Why do Catholics have more books in our Bible?
A Catholic Bible has 46 books in the Old Testament and 27 books in the New Testament. But a Protestant Bible has only 39 books in the Old Testament. The Protestant Bible does not contain Sirach, Ecclesiasticus, Wisdom, Judith, Tobit, Baruch, 1 Maccabees, and 2 Maccabees. These are known to Catholics
as the Deuterocanonical (Second Canon) books while they are known to Protestants as the Apocrypha  ("not authentic"). Why is there a difference?

There was much discussion and debate in the early Church about which books were inspired by God. It was important to establish a single, authoritative definition of what was (and what was not) Sacred Scripture. Some in the early Church argued for the inclusion of the Gospel of Thomas, the Shepherd of Hermas and other works that the Church ultimately rejected. As well, many insisted that the Book of Revelation, 2 Peter, 3 John were not inspired, yet they were, in the end, accepted by the Catholic Church as canonical. The Council of Rome in 382 was the first to produce the list of books used today in the Catholic Bible. This list did not end the discussion and debate, but the list was confirmed by at least 4 other major Church councils between 393 and 1441. (You can read more details here.) Thus, the definition of Sacred Scripture - also known as the canon - was widely accepted by the Church for centuries before the Protestant Reformation. Indeed, when Johannes Gutenberg printed his Bibles they include the full canon of 73 books.

During the Reformation, Martin Luther and other Protestant leaders questioned whether some of the Old Testament books were truly divinely inspired. They disagreed on the exact list of books they questioned, but eventually 7 books were excluded from the Protestant Bible. Martin Luther used the argument that these 7 books taught doctrine that was unscriptural. The Catholic Church has always conformed her doctrine to the Word of God; Luther tried to conform the Word of God to his own doctrine. He also tried to remove James and Revelation from the New Testament but was dissuaded by his fellow reformers. He called the Letter of James an "epistle of straw" because it plainly refuted his claim that man is justified by faith alone. (See James 2:24)

To respond to the confusion of the Protestant revolt, the Catholic Church covened the Council of Trent in 1556. One of the questions the Council dealt with was the contents of the Bible. As with many other issues, the Church leaders prayed and looked to Church Tradition and the practice of the Church Fathers in order to find the answer. The Council infallibly declared the canon to be the same list that was originally produced by the Council of Rome. (See the Canon of Scripture in paragraph 120 of the Catechism of the Catholic Church.)

You may hear claims that the Catholics "added" seven books to the Bible after the Reformation. However, since the Catholic Church can trace its canon back to the fourth century, it is clear this claim is untrue. The Council of Trent did not add anything to Scripture - rather it reaffirmed the canon already long in use by the Church. (A more extensive response to this claim is available here.)

For example, Luther denied the existence of Purgatory. The Book of 2 Maccabees 12:43-46 promotes the practice of praying for the dead. Because those in heaven have no need our prayers and those in hell are beyond the help of prayer, the Church reasoned that there must be a third state in which the dead may benefit from the prayers of the faithful and that was Purgatory.

For common objections to the Deuterocanonical Books and answers, click here.