I have seen "evidence" that we know with a great degree of certainty and accuracy what the original New Testament bible said. This is to say, we know what the original authors wrote. I'm not sure how accurate these claims are as they seem to come from biased sources. Here are a few:
The short answer is no [the bible was not corrupted]. To answer this question in more detail, let me
give you some background. The New Testament is an ancient book.
During ancient times, there were no Xerox copy machines, and the way
the Bible was preserved was through hand by hand copying. As a result
of this copying process, errors would occur by accident or intention.
However, these errors in the text do not affect any major Christian
doctrine such as the Trinity, Deity of Christ, salvation by faith
alone, etc. Unfortunately, we do not have any original copies of any
of the books of the New Testament. In other words, we do not have “the
original manuscript copy” of Paul’s Epistle to the Romans or an
original copy of the Gospel of Matthew, etc.
There are way more copies of the biblical manuscripts, with remarkable consistency between them, than there are for any of the classics like Plato, Aristotle and Socrates. "There is no body of ancient literature in the world which enjoys such a wealth of good textual attestation as the New Testament." F.F. Bruce, The New Testament Documents: Are They Reliable?
To be clear I'm not asking if the events talked about in the bible are true. I'm asking: Do we know the words used by the original authors of the New Testament?
Do we know the words used by the original authors of the New
The answer is a qualified yes.
As tniles09 comments, the (scientific) discipline that studies this is called Textual Criticism, and has had an enourmous development, especially during the last two centuries. You can check the current consensus of the scholars in the majority of serious books on the subject (you can discard the obviously "interested" ones, be on the christian apologetic side, in the atheist side, or in the mere sensationalist-commercial side).
To summarize, and restricting to the four gospels (main part of the New Testament), we can state with high degree of confidence:
The four gospels were written in Greek, in the date range 60-100 AD
(first Marc, then Matthew and Luke, last John)
The oldest manuscripts we have now are small fragments, the earliest complete manuscripts of the gospels are from the third or fourth centuries. They are, relative to other antique texts, abundant.
The "original" texts can recovered with high degree of confidence (only some words or verses are in doubt). Errors in copies (both unintentional or intentional interpolations) are easily identifiable, in general. The reconstructed texts essentially coincide (translations aside) with the "official/vulgar" texts of the Bibles used always by the Christian churches.
I quote "original", because your assertion "that is, we know what the original authors wrote" needs some qualification. We need to relativize our modern ideas of literary autorship and originality (the individual that sits alone in his study, and writes "his" own words). Twenty centuries ago, things were different, in many senses: oral tradition played an important part (not only as a trasmissions of facts/tales/ideas, but as a trasmission of texts), the tasks of literary creation (and reelaboration, conservation, trasmission) was more a community thing. Think for example of the "synoptic problem": parts of the first three gospels seem like copy-paste from others, and yet they differ (even sometimes contradict) with each other, and each one has its own style: this would be almost incomprehensible in our modern frame of "autorship" (either we have four individual and honest authors... or we have not; if they are narrators of the life of Jesus, we expect them to tell us the same things using different words; the gospels, instead, sometimes seem to be using the same words to tell different things).
We don't need to go to the extreme, and reject the notion of individual authors: textual criticism asserts that, in spite of the above, each one of the gospels has an individual author, in the literary sense. But this must be weighted against the other elements: they were antique authors, they regarded themselves as faithful voices of a community. Granted this, then yes, we can be reasonably sure that when we read the current texts of the New Testament, we read "what they wrote".
We are not here saying that
the original authors were indeed named Matthew, Mark, Luke, John - or that they are some identifiable persons (that Mt. and J. were disciples, for example). We don't know that, we know practically nothing about the concrete authors, and we know that is was an antique custom to use pseudonyms to enhance a book authority. (What we know is that Luke was the same author of the Acts book)
the events narrated are strictly historical, in the modern sense of the word
the authors were (or claimed to be) "inspired by God" or that the texts are somehow "inerrant" (those are theological questions)