Before the Reformation, the Western Church used the Vulgate Bible, which was in Latin. It was a closed book to most of the populace. An 'infallible' test for revealing a heretic to Roman Catholic authorities in the Middle Ages was to see if they possessed, or even knew any part of the Bible in their own language.
The King James Version comes down through the Hebrew-Masoretic Texts (Old Testament) and Koine Greek Texts (as written by the apostles and those who knew Jesus.) This formed the original Old Latin Version (as opposed to the one corrupted by Jerome and adopted by the Catholic Church - the Latin Vulgate). It became known as the Textus Receptus.
The Bible was first translated into English in 1382 by John Wycliffe, who worked from the Latin Vulgate. Wycliffe's Bible was immediately outlawed by the Catholic church, and anyone caught reading or reciting biblical passages in English faced imprisonment and even death for heresy.
In 1525 William Tyndale completed the translation of the New Testament from its original Koine Greek into English. He also translated most of the Old Testament from Hebrew to English, but was unable to complete the work before his death in 1536 (he was burned at the stake as a heretic).
Guttenberg's first printing job was the Bible, in 1453. It was not the Vulgate. This one had been translated from the original Hebrew, Greek and Aramaic, known as the Majority or Traditional Text. Erasmus published the first printed Greek New Testament in 1516, then came the Tyndale/Coverdale Bibles in 1525; the Geneva Bible in 1560; the Bishops' Bible in 1568 and then King James I of England & VI of Scotland commissioned the KJV which was published in 1611. The KJV had used the Hebrew Masoretic Text and the Greek Received Text alongside working from the Bishops' Bible. You can get a list of the various translators at http://www.jesus-is-lord.com/transtoc.htm
All other Bibles come down through the Latin Vulgate, Codex Vaticanus, the Codex Sinaiticus, Codex Alexandrinus. The Catholic Church helped to preserve these texts while at the same time murdering those who would preserve and preach the texts derived/descended from the Textus Receptus.
The group that put together the NIV used the Westcott and Hort manuscripts to create their version, making well over 30,000 changes to the word of God (when compared with the KJV), even removing verses at times (eg Matthew 18:11 among many omissions). The King James Version, commissioned by its namesake, was finished in 1611, with the Apocrypha included, thought to be because of King James' Catholic wife. The 1669 version of the King James removed the Apocrypha and tweaked some of the minor misprints.
That is a bit of history for you and I hope it helps you understand the differences. Nearly all the Christians I know use BOTH the KJV AND modern ones using the other pedigree of manuscripts. There is no single "right" translation! Ordinary Christians like you and I cannot know how best to choose, but the Holy Spirit guides us. He uses all different kinds of translations to 'speak' to seekers. Whatever part of God's written word a person comes across, the Holy Spirit can use to convert them and teach them. I've even known the notoriously corrupted Jehovah's Witness translation be used to show people the deity of Christ! Despite their efforts to water that down, it's still there and the Holy Spirit brings necessary points to the attention of people. Don't weep! Just thank God that we have such an abundance of Bibles today!