There's an entire field of study called "textual criticism" devoted to this sort of question. On the broadest scale, there are about 1.25 million pages of anci

There's an entire field of study called "textual criticism" devoted to this sort of question. On the broadest scale, there are about 1.25 million pages of ancient Greek New Testament text, made up of everything from tiny fragments to complete copies, spanning the course of several centuries and initially spread over three continents. Among these 1.25 million pages there are about 250,000 errors (places where one manuscript differs from another), the vast majority of which are simple spelling mistakes or grammatical mistakes (often repeated in every manuscript from a particular region.) So there's about one mistake for every 5 pages of ancient text. Moving a bit more narrow: the New Testament of the King James Bible was translated using an incomplete set of Greek Manuscripts which were supplemented with translations from Latin back to Greek, which is collectively called the "Textus Receptus". Most modern translations are made using what's called the "Majority text", which is an attempt to uncover the origin of various textual differences by looking at timelines and common patterns in variants (like dropping words that start with the same letter as the previous word, or much more sophisticated methods like taneliv mentioned in another comment). There are around 2,000 variants between the Textus Receptus and the Majority text (there's a comprehensive list in the back of Jay P. Green Sr.'s "The Interlinear Bible".) The Codex Sinaiticus is more similar to the Majority than to the Textus Receptus, and 2,000 total variants is a pretty good estimate for how different it would be from what was used to translate the KJV. As before, the vast majority of the differences are spelling errors and such that wouldn't even survive the translation process (for example, in Matthew 1:6 there's a spelling variant of "Solomon" in some texts.) There are less than 10 differences large enough to be worthy of discussion, which are listed at the end of the wikipedia link wl posted in a sibling comment -- the longer ending of Mark and the story in John 8 about the woman caught in adultery, for example. All of the doctrines I'm aware of that are expressed in the disputed passages also find fairly broad support in other passages, as well as in other ancient church writings that aren't part of the Bible, though not necessarily as explicitly. So the overall answer to "how different" is "enough to show the text wasn't perfectly stable, but not enough to overturn any widespread doctrines or beliefs". (If you're interested in seeing the practical application of the process of textual criticism, try the NET Bible at net.bible.org -- any of the footnotes marked "tc" are about textual criticism, and they generally explain why the translator chose a particular variant, and in some cases they'll point to a book or journal article for deeper discussion. It's not perfect, but it'll give you an idea of the overall state of knowledge.)