The Protestant Bible has 66 books. Should we read apocryphal books (e.g. 1&2 Maccabees and Gospel of Thomas)?
put on hold as primarily opinion-based by curiousdannii, Mr. Bultitude, fredsbend, bruised reed, Matt Gutting 11 hours ago
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You don't need to (as in should), but you can if you want to. Don't allow them any special authority if they're not in your Bible; use common sense. Apocryphal books and other writings of the time might be interesting in many ways, e.g. historically.
There's an important distinction to be made between 1&2 Maccabees and the Gospel of Thomas. This distinction also tells you a lot about how useful a certain book would probably be to read.
Old Testament apocrypha / Deuterocanonical books
1&2 Maccabees aren't included in the Protestant Old Testament, but Roman Catholics and most Orthodox Christians consider them canonical. They weren't in the Hebrew Bible, thus they're called deuterocanonical as opposed to protocanonical. As Raphink points out in his answer, these books were written later than the protocanonical books and thus couldn't be included in the Hebrew Bible.
Protestants consider deuterocanonical books Old Testament apocrypha, i.e. books that don't have divine authority but are relevant with regard to pre-New Testament history. Martin Luther said about them:
Useful and good to read -- but not divinely inspired, according to Protestants.
There's a very broad consensus between Christians of different denominations on what books are included in New Testament. In fact, there's practically no disagreement here. Luther was probably the most vocal questioner of the authority of James, Hebrews, Jude and Revelation, but even he didn't exclude them from canon. Neither does any major denomination nowadays consider any extra books to be part of New Testament.
The Gospel of Thomas is one of the better known writings belonging to New Testament apocrypha. It might also be one of the more interesting ones. However, keep in mind that no one notable considers it part of the Bible. Neither is there any church-father, reformer, founder of a major denomination or such saying that it's "useful and good to read".
There are many other books considered New Testament apocrypha. I'll say from personal experience that not all of them are worth reading.
Old Testament apocrypha are considered part of the Bible by some and "useful and good to read" by some.
New Testament apocrypha are considered neither.
Treat them as you would any other work by an author who claims to be Christian. Weigh what is said carefully against scripture and evaluate it for what value it has.
Knowing why it was rejected (was it heretical or known to be falsified or simply not surely inspired) might help in such an evaluation.
Personally I have found the extra-biblical works quite interesting in their own right. Quite like the writings of the early church fathers, which are really very informative.
As has been said already, you can read (and it can be interesting) the apocrypha. Just don't consider them as authoritative.
I'd like to complete the other answers by stating a difference between the Old Testament apocrypha and the New Testament apocrypha.
The Old Testament apocrypha, such as the Maccabees, are not included in the Jewish Canon (and thus not in the Protestant Bibles either) mostly because they were too recent (or even not written yet, depending on when you consider the Jewish Canon was fixed) to be included.
For that reason, Old Testament apocrypha is very interesting historically since it tells you about what happened between the end of the Old Testament and the beginning of the New Testament. For example, it explains about the origin of Hanukkah, a day that was already celebrated at the time of Jesus. You can think of Old Testament apocrypha as an interesting part of history.
On the other hand, most of the New Testament apocrypha are books that were considered non interesting, not God-breathed or even heretic by the early Christian church.
You're more likely to find ungodly ideas or twisted scriptures in New Testament apocrypha (such as the Gospel of Thomas or of the Women) than in Old Testament apocrypha. You can think of New Testament apocrypha as alternative accounts of Jesus' life and possibly heretic theology.
The current Jewish canon did not arise until after the time of Christ. The Old Testament apocrypha were in the Greek translation of the Bible known as the Septuagint, which is older than any existing version of the Bible except for books found relatively recently among the Dead Sea Scrolls. The standard Hebrew version of the Bible that exists is much newer than the Greek version. The early church, like most Jews at the time, accepted the extra books as scripture, and so should Protestants.In fact, the Septuagint was the version of the Old Testament that was read by New Testament authors. Rejecting the books written in Greek is just a current Protestant tradition.