The Muratorian Canon (or Fragment) is a list of Scriptural books dating from the 2nd century. Because it is the only such list from before the 4th century, some scholars want to give it a 4th century date.
Personally, I think its statement that Pius was recently bishop of Rome (AD 157-170) should be taken at face value. There's nothing about the books chosen in this canon that makes it unlikely to be 2nd century. You can get a similar canon by picking quotes out of Irenaeus or Clement of Alexandria, whose writings both belong to the late 2nd century.
Every canonical list through the Council of Nicea (AD 325) can be found at Quotes About the Scriptures.
This translation of the Muratorian Canon was originally from the Ante-Nicene Fathers, volume V. I've updated it to modern English, as is my habit on this site.
… those things at which he was present he placed thus.
The third book of the Gospel—the one according to Luke, the well-known physician—was written by Luke in his own name, sequentially, after the ascension of Christ at the time when Paul had associated him with himself as one studious of righteousness. [Luke] himself did not see the Lord in the flesh. As he was able he began his narrative with the birth of John [the Baptist].
The fourth Gospel is that of John, one of the disciples. When his fellow disciples and bishops pleaded with him, he said, "Fast with me for three days, and then we'll tell each other whatever may be revealed to any of us." That very night it was revealed to Andrew, one of the apostles, that John should write everything in his own name as they remembered them.
As a result, although different points are taught to us in the various books of the Gospels, there is no difference as regards the faith of believers. In all of them under [the influence of] one imperial Spirit, everything is told which concerns the Lordís birth, his suffering, his resurrection, his conduct with His disciples, and his twofold coming: the first in the humiliation of rejection, which is now past, and the second in the glory of royal power, which is still in the future.
What a marvel it is, then, that John presents these various things so consistently in his letters, too! He says in his own person, "What we have seen with our eyes, heard with our ears, and our hands have handled, that have we written." For in this way he testifies that he is not only the eye-witness, but also the hearer. Besides that, he is also the historian of all the wondrous facts concerning the Lord in their order.
In addition, the Acts of all the Apostles are comprised by Luke in one book and addressed to the most excellent Theophilus, because these events took place when he was present himself. He shows this clearly, i.e., that the principle on which he wrote was, to give only what fell under his own notice by the omission of the suffering of Peter, and also of the journey of Paul when he went from the city of Rome to Spain.
As to the epistles of Paul: again, to those who will understand the matter, they give their own indication of what they are, from what place or with what purpose they were directed. He wrote first of all—and at considerable length—to the Corinthians, to check the schism of heresy; then to the Galatians, to forbid circumcision; then to the Romans on the rule of the Old Testament Scriptures—and also to show them that Christ is the first object in these, which it is necessary for us to discuss separately.
The blessed Apostle Paul, following the rule of his predecessor John, writes to no more than seven churches by name, in this order: the first to the Corinthians, the second to the Ephesians, the third to the Philippians, the fourth to the Colossians, the fifth to the Galatians, the sixth to the Thessalonians, the seventh to the Romans. In addition, though he writes twice to the Corinthians and Thessalonians for their correction, still it is apparent—by this sevenfold writing—that there is one Church spread abroad through the whole world. John, too, in the Revelation, although he writes only to seven churches, yet addresses all.
[Paul] wrote, besides these, one to Philemon, one to Titus, and two to Timothy, in simple personal affection and love indeed. Nonetheless, these are holy in the esteem of the catholic [i.e., universal] Church, and in the regulation of church discipline. There are also in circulation one to the Laodiceans and another to the
Alexandrians, forged under the name of Paul and addressed against the heresy of Marcion. There are also several others which cannot be received into the catholic Church, for it is not suitable for gall to be mingled with honey.
The Epistle of Jude, indeed, and two belonging to the above-named John–or bearing the name of John–are reckoned among the catholic epistles, along with the book of Wisdom, written by the friends of Solomon in his honor.
We also receive the Revelation of John and that of Peter, though some among us will not have this latter read in the Church. The Pastor, moreover, did
Hermas write very recently in our times in the city of Rome, while his brother, bishop Pius, sat in the chair of the Church of Rome. Therefore it also ought to be read, but it cannot be read publicly in the church to the people, nor placed among the prophets—as their number is complete—nor among the apostles to the end of time.
Of the writings of Arsinous, also called Valentinus, or of Miltiades, we receive nothing at all. Those are also rejected who wrote the new Book of Psalms for Marcion, together with Basilides and the founder of the Asian Cataphrygians.
So the books listed in the Muratorian Canon are as follows:
This leaves out Hebrews, James, 1 and 2 Peter, and 3 John. That's not unusual in the west in the 2nd century. In fact, what might be most unusual is his inclusion of 2 John! (Of course, we don't know it's 3 John he's leaving out. He doesn't say which two letters of John were being read.)
The inclusion of the Wisdom of Solomon as a New Testament book in the Muratorian Canon is interesting as well. Every other list I've found, up to about AD 400 either doesn't mention it or puts it among the Old Testament writings.
For all the hype surrounding the Gospels of Thomas and Judas nowadays, they get almost no attention from pre-Nicene writers. There's a revival of gnosticism being sparked by Elaine Pagels and Hugh Schonfield. It's a bunch of nonsense. Dan Brown revived some of Hugh Schonfield's ideas in his The Da Vinci Code, but those arguments are very weak.
All of these people love to spread the myth that the Council of Nicea banned gnostic books from the Bible. This simply did not happen. As you can see, the Muratorian Canon makes no mention of these gnostic writings, and you'll find that no other list of canonical books from before the Council of Nicea includes them, either.