The fact is that for practically all ancient writings, we no longer have the original manuscripts. We don't have them for the writings of Homer, for Virgil, or for Plato, either. So should we just give up on all ancient writings, say "we don't know what they originally said, so they're of no value to us"? Of course not. While there is no way to determine with 100% certainty what an ancient writing originally said, there are ways to determine how reliable a copy can be considered to be. When scholars have copies of ancient writings, they can:
A) Compare the different copies that they have (if the copies are wildly different, then obviously many changes were made)
B) Determine how much time has passed between the time the texts were written and the earliest copies (the greater the amount of time, the more likely the possibility of changes having happened)
C) Look at where the various copies were found (if all ancient copies were from one specific area, the easier it would have been to make changes that were reflected in all existing copies)
D) Look at references to the ancient texts in other works, if any (if other authors refer to or quote from the ancient text, but they say something different than what our copies say, then clearly someone changed things somewhere along the line).
The result of studying these factors for the Biblical texts, and comparing them to these factors for other works like those of Homer, Virgil and Plato, tell us something very interesting. There is far, far greater manuscript support for the Biblical texts than there is for any other ancient writing. There isn't even a close second.
We have around 24,000 ancient copies, either partial or complete, of the New Testament. About 5600 of those are in Greek, the language the NT was originally written in, and provide us with the best comparisons. What ancient text comes in second, then? That would be Homer's "Iliad", of which we have 643 ancient copies in the original language, and is generally considered to be the most well-preserved non-Biblical text. And how soon after the original were they written? For the New Testament, the earliest fragment would be a difference of 30 years for a part of John's Gospel. For most texts, we're talking about 150-200 years between the writing and the earliest copies. For Homer's "Iliad", the earliest fragment dates to about 500 years after it was written. As for comparing the different copies, if we do so for the New Testament writings, we find them to be 99.5% similar, with the only differences being primarily in wording (like saying "Christ Jesus" instead of "Jesus Christ"), and not any differences in actual meaning. Biblical critics like to point out that there are 150,000 variants between the copies we have. While this is technically accurate, it's also misleading. Of those variances, the vast majority are simply minor spelling errors or different wording for the same idea. Only about fifty of those variances are in any way problematic, and even those don't have variances in issues relating to Christian doctrine or commandments. The reason we have so many variances, quite frankly, is that we have so many ancient copies. With 5600 ancient Greek copies, of course we're going to have variances. If we'd had only 100 ancient copies, we'd obviously have far fewer variances between them. Essentially, bible critics are trying to punish the New Testament for having so many ancient copies! Like I said, the New Testament writings are 99.5% similar between ancient copies. For Homer's "Iliad", it's only 95%.
Also, I mentioned the idea of looking for references to the text in other ancient writings. The early church fathers were, of course, fond of quoting from the New Testament. There exists almost 86,000 quotations from the New Testament in the works of early church fathers. In fact, we can reconstruct all but 11 verses of the New Testament from external sources from within 200 years of the writing of the New Testament. And as for copies being found in different locations, including Syria, Babylonia, Galatia, Asia, India, Rome, India, Egypt, Greece, Carthage, Tarshish and Macedonia.
If those doing the copying were making changes as they saw fit, we would have ended up with about 1000 or more vastly different gospels. You see, the copying was done by many different people in many different places independently of one another. Unless they'd somehow conspired among each other to make the same changes, their changes would have been different. Instead, even though there are many different translations of the Bible, the Bibles are generally in unison about the events and the spirit of what is said. Researchers actually managed to take 2 groups that had been isolated from each other for over 1000 years, copying and re-copying their own Bibles. The end results of each of their gospels DID contain some differences, but only in 8 letters, and absolutely no differences in the gist of what was being said. Those doing the copying took great care to preserve the integrity of what was being said. They knew that to change God's word to suit their own purposes would have been pointless and cruel.
The fact is that there is no evidence that ancient scribes were making intentional changes as they were copying the Bible. If they had, we would have ended up with severe variances between the copies we have, since there were many different people copying the texts in many different places.