Catholics often argue that without their Church, no one would know which books belong in the Bible. This is rather silly, considering the canon existed before the Catholic Church, but more to the point, canon is canon. In a previous article, I showed that the inspiration of scripture means the scriptures were canonical even before they were compiled into a single volume. The fact that they are now included in one book is helpful, but not essential for canonicity. If you take a book out (for sake of argument, let's say Genesis), Genesis is still canon because it is still inspired. If you add a book in, like Judith, it's still not canon because it's not inspired. Ironically, Catholics actually did this in 1548, but Christians didn't follow suit, so clearly Christians aren't following Catholicism anyway.
To illustrate this, the header image contains four DVDs, all staring Rowan Atkinson. Me and my brother are both fans of Rowan Atkinson. As my brother is severely autistic, he is especially obsessed. Recently, he told me there were only 3 Johnny English films, and I joked about how, actually, there are 4, because Mr. Bean is a prequel.
Now, let's imagine a bizarre scenario in which Johnny English became a religious figure. As is the case with most movies, Johnny English can be bought as separate DVDs, but the image actually shows my two copies which come from a box set. We now have an excellent analogy!
First, anyone can tell the difference between that which is canonical to Johnny English and that which isn't. You don't even have to like Johnny English, and even if you were to get rid of every possible reference to the title (let's be honest, dead giveaway...), anyone could watch the movies and see "hey, this is connected to this". They could also watch Mr. Bean and say "this isn't connected to Johnny English." When the third movie comes out on DVD, you can immediately add it to your collection.
[Post publication note: This article was originally written before the 3rd Johnny English came out on DVD. Rather than mess with the article, I have decided to leave the text unedited, as the point I made still stands.]
Just as movies are easily distinguishable according to their canons, so also is the Bible distinguishable according to its own canon. Obviously, when it comes to the Bible, it's a lot harder (which is why Christians can be grateful that the hard work has been done for us). As an example, there is some dispute about the book of Esther, and arguably for good reason. It doesn't even directly mention God. But God's presence within the story is clear, the historical accuracy is impeccable, and of course the Jews, to whom the oracles of God had been entrusted, included it in their canon (which it should be noted Jesus implicitly endorsed and never once disputed). One can therefore conclude that Esther is canonical.
Although the Bible never gives its own list of what ought to be included within, there is a process that would lead most Christians to come up with the same books. There's a reason Christians don't typically cut up their Bibles or produce several different canons. Put simply, the 66 books we have are correct. The work has been done for us (and not by the Catholic Church), but even if it had not, it could be done again.