Should a Protestant read the apocryphal books of the Bible? The Protestant Bible has 66 books. Should we read apocryphal books (e.g. 1&amp;2 Maccabees and Gospel of Thomas)?
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&amp;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&amp;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:


  Apocrypha, that are books which are not considered equal to the Holy Scriptures, but are useful and good to read.


Useful and good to read -- but not divinely inspired, according to Protestants.

New Testament apocrypha

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.

Summary

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.