Because of the time period, some people associate Shakespeare with the KJV. However, the KJV was published in 1611. Shakespeare did most of his work between 1589-1613 and he died in 1616. The Bible with which Shakespeare would have been most familiar was the Geneva Bible.
For those of you interested in learning more about this topic and more about the KJV and its history, the Manifold Greatness Blog is a good source. Read more about Shakespeare and the Bible on one of their latest posts: manifoldgreatness.wordpress.com/2011/11/30/shakespeare-and-the-king-james-bible-ships-passing-in-the-night/