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120 year old Bible title page - photo by Wonderlane - cc-by

You might assume that a book as old as the Bible is available for anyone to copy freely, but that is not always the case. When we access the text of the Bible it is not from the original scrolls but from a more recent translation or rewriting – and some of those versions are under copyright.

Copyright even subsists in some very old versions, such as the Authorized King James Version published in 1611 – but only in the United Kingdom as the rest of the world does not recognize this British Crown Copyright.

Other than the KJV, Bibles published before 1923 are free of copyright in most countries. An example of a copyright-free Bible is the 1901 American Standard Version.

In some cases, Bibles published in or after 1923 are free of copyright because their creators have explicitly waived copyright. The World English Bible is one such version.

In most other cases, Bibles published in or after 1923 are subject to copyright. In many cases the coypright holders defend their copyright vigorously.

Some more information is provided in the answer to this Google Answers question.

StudyLight.org provides a comprehensive list of English-language Bible translations, and includes information about the copyright status of each of these.