It is important to understand that we do not have an "original copy" of any book of the Bible. What we have are copies of copies of copies... (manuscripts), from which "Textual Critics" seek to ascertain the original wording. It is the original wording that most Bible scholars hold to be perfect and inspired by God.
Many modern Christians view "The Bible" that is sitting on their shelves as the perfect, exact word of the living God, but this doctrine is a bit off. What is sitting on your shelf is an English rendition of a particular translator's interpretation of the group of manuscripts he studied when writing his translation. (NOTE: The Bible on your shelf is completely sufficient for understanding God's message to us in 99.99% of cases.)
The books of the Bible were not originally divided into verses - this happened around the 16th century. This was a period in time when a very limited set of manuscripts were available for translation. The numbering scheme was, of course, based on those manuscripts which were available at the time. The KJV is one of the translations written around this time. (It is very interesting to look at how few manuscripts the KJV is based on, but that is a huge volatile topic that I won't go into here.)
Since that time, thousands of manuscripts have been excavated, which have given us more insight into what the original wording might have been. Modern translators (e.g. the NIV translators) seek to faithfully handle the word of God by considering as many reliable manuscripts as possible during translation - which is exactly what the KJV translators sought to do in their day (they just had far fewer manuscripts to work with.)
Contrary to what the KJV-only camp would have you believe, the NIV translators are not trying to lead you into a fiery demise by deceiving you with false translations. Many of the so-called "missing verses" are referenced in the side-column of your NIV Bible (see here). The only reason they were left out is that the translators of the NIV honestly believed that the evidence was overwhelmingly against those verses being part of the original writing.