The KJV isn't an accurate translation, it's not even a good one. There are better translations these days based on better scholarship and older source texts. For those who claim the KJV is what American Christianity is built on, no it actually isn't. The Puritans favored the Geneva Bible, and detested the Church of England's KJV Bible.
Why do people put so much stock by the KJV? What makes it so special?
Mainly because the KJV is one of the most literal translations of the Christian Bible, the other is the Revised Standard Version which translates to modern English as spoken in the US. The Revised Standard Version is the most widely used Bible in the classroom.
Short history lesson on Bible translations.
There were four major translations in ancient times, all from the Hebrew original, the first two were done by Jewish scholars and the last by Christian scholars.
1. The first and oldest was into Greek, commonly called the Septuagint was done in around 3rd century BCE
2. Targum was a Aramaic translation dating from the 1st-6th century CE. It was not a single work but a series of works. We have in our possession 3 different translations of the Torah in Aramaic. One is a relative literal translation and the other 2 are very expansive. Paraphrasing includes additional material that is not in the original Hebrew text.
3. Pe****ta. A Syriac translation (4-5 century CE)
4. Vulgate, a Latin translation (Catholic) (405 CE)
As I said above the KJV and the RSV are the most correct literally. The Jewish Publication Society's Tanakh departs from the text literally and uses a idiomatic style. Everett Fox's "The Five Books of Moses" is the most literal translation of the Torah.