Canon for both Testaments was pretty much agreed on through usage by the time the various canons were sealed. I'm a little rusty on my Hebrew history, but I know that the Old Testament was canon by 250BC (my assumption is that the Temple priests and scribes set it), when the Septuagint was produced. The New Testament canon was set in the late fourth century AD by the leadership of the church.
The books that were "left out" had various problems. Some were obviously Gnostic or wildly legalistic in their bent, and the overwhelming majority weren't written until well after the time of the Apostles and their contemporaries - the Gospel of Thomas, for example, isn;t likely to have been written before about 250AD.
You might want to try googling for the Councils of Hippo, Carthage and the (Jewish) council/school of Jamnia/ Yavneh. Or Wikipedia is your friend for them.
Ah, but they can't possibly have been 'good men' since everyone knows that Constantine founded the Roman Catholic Church so they were all "Nassty cruel Catholicses; we hates them, we hates them forever!" by then
Actually nobody knows exactly if the current cannons are corrupt, correct or not or whether the Council of Nicea was corrupt from the influences of Constantines emmasaries.
Our only hope is God's promise that all scriptures is given by inspiriation of God. I would put my hope in God more than earthly opinions; and thereby denigrate God's power. History teaches us a lesson by showing how people would destroy the Word; but has it really happened? I don't think so.
Ah, but then you create yourself a problem: how can we as mere mortals rely on the Bible that sits on our bedside table (as mine does and I'm sure yours does too) as being the Word of God, if we don't know whether it contains the correct material (whether or not because we have doubts as to whether the men who decided what material would go in it were corrupt or not)?
Setting aside the painfully pointless argument over the acceptablility of the Council members who set canon, we can be reasonably certain that the content of the canonized books is accurate. There are more extant manuscripts for the Bible than for any other ancient work, by an overwhelming margin.