In my recent introductory New Testament class, my professor had students grapple with issues of NT authorship. I was tangentally aware that these debates, but had not addressed them in any sort of depth.
It could prove frustrating. There seems to be a school of thought which says, "This epistle claims to be written by Paul, fits easily into known Pauline theology, and was recognized by the early church as authentically Pauline, therefore it could not have been written by Paul." Even by the standards of secular scholarship many of the doubts of NT authorship seemed flaky.
Many call into question the ability of semi-literate Galilean fishermen to compose elegant Greek prose. From a secular point of view, this is a reasonable concern. From a Christian point of view, it is not, since it doubts the ability of the Holy Spirit to work beyond the intellectual confines of the man with the quill in his hand.
Today, in my daily reading, I encountered a verse which would support my understanding of the Holy Spirit in this process of Biblical composition. Early in Acts, Peter heals a lame man, for which he and John are hauled before a Temple court to answer for the crime. Peter gives an eloquent defense of their actions, to which the priests are surprised:
Now as they observed the confidence of Peter and John and understood that they were uneducated and untrained men, they were amazed, and began to recognize them as having been with Jesus.
UPDATE: In the comments, Greg Hazelrig brings up a common argument for the legitimacy of pseudonymous NT works:
I was taught that (and this was in a Gospel of John class) sometimes the disciples of an apostle would write in that apostle's name as a tribute to the apostle. So in other words, it was not seen to be fraudulent, but instead in honor of the apostle.
If this was a common practice, then we would have pagan works from the same period that reflected it: a work written by the spiritual successors to a revered but dead leader to an audience that knew that it was not written by the ascribed leader, but still accepted as legitimate scripture.
To my knowledge, there are no such works. When I asked my NT professor, who advanced the argument, if he could name one, he could not. Unless scholars can find such pagan works, this argument is groundless speculation.