This will be the starting point. Let's start with these 10 most popular Bible versions mentioned on Twitter in 2010:
KJV is the King James Version and the text itself is in public domain. However, certain formats of packaging the data may be copyrighted. See the Bible download page here for freely available KJV Bible text.
ESV is the English Standard Version, copyrighted by Crossway, a publishing ministry of Good News Publishers. According to their Permissions page, "Crossway allows you to access the ESV Bible text from our server and include it on your website or app, free of charge for non-commercial use. To learn more or register for the API, visit api.esv.org." For other usage, contact Crossway at crossway.org/permissions/digital/
NIV is the New International Version, with copyright held by Biblica, Inc. To obtain licensing information and permission to use for commercial or non-commercial purposes, contact the corresponding point of contact listed on the page, How do I license the NIV for additional use? Note there are different contacts for commercial use in the US and Canada; commercial use in the UK, EU and EFTA; and, non-commercial use.
The Message is a popular reading Bible translated by Eugene Peterson; its copyright holder is NavPress and they're represented by Tyndale House Publishers, Inc.. According to their Permissions Information page, "Permission to quote from THE MESSAGE in projects produced for sale may be accompanied by a fee. The amount of this fee is based on the percentage of the total text that is represented by quotes from THE MESSAGE as compared to the total amount of your text in the final product, the distribution of that material, and whether it is for commercial or non-commercial use. All fees are established to protect our copyrighted material." To obtain written permission, fill out the Permission Questionnaire. The more details you provide about your project, the quicker they can process your request. Allow 2-4 weeks for a response.
More to come...
[update 1/07/2019] See the next blog post in this series for the one place to get easy access to multiple Bible versions for software development. This is a huge time saver!