If the Bible has been changed over the years, can we still trust it? I read that there are passages that exist today that are not in some of the oldest scrolls.  Since these passages were added along the way&mdash;maybe to help explain something&mdash;can we trust that the Bible is the same original word of God?

These possible later additions include the following:


the ending of Mark, see Mark 16.
Jesus sweating blood in Luke (Luke 22:43–44).
the story in John of the woman taken in adultery, the Pericope
Adulterae.
an explicit reference to the Trinity in 1 John, the Comma Johanneum.


While many of the changes are small and not important, "Comma Johanneum" is the only place in the entire Bible that the Trinity is directly addressed.  So if this wasn't part of the original text, that would be problematic.

If the original scrolls were inspired, why didn't God preserve them?  Alternatively, how can we trust that the Bible we hold in our hands today faithfully represents the originals?
It's important to understand something about the origins of the Bible. The authors of the various books within it did not sit down to write "The Bible". They intended to write stuff that would be helpful to other people for various reasons: in the case of the Gospels, so people would know the true story of Jesus' life and teachings, and for the letters to instruct the recipients in Christianity. These documents were not collected to form the Biblical Canon until much later, around 400AD.

It is certainly true that there exist manuscripts of New Testament documents (primarily the Gospels and Acts) which show variations. Some either have or have not certain passages: some use slightly different wording. However it is important to note that the vast majority of these 'differences' come from before the period where the documents were collected into 'The Bible'. These differences make a lot of sense. If you have a document that describes the life of Jesus, and you also know of a story that you are certain is true about Jesus, you might well add it in. Of course if people disagreed with you about the validity of the story they would not copy your document.

Once the Biblical canon has been more-or-less defined the variations become much less - again unsurprising, since making changes to the Word of God is a much more serious matter than to a 'true story'. Such differences as exist are likely copying errors.

So TL;DR : No, the Bible has actually changed very little since it became The Bible. Before that there were different manuscripts with some differences, but in reality not a lot of variation.