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I have used PocketBible Bible Study by Laridian, Inc. for years ever since first using it on my Palm PDA's:
https://play.google.com/store/apps/details?id=com.laridian.pocketbible
I'm a big fan of Pocket Bible. I've been using their software for about 15 years. You do pay for the bibles, commentaries, devotionals, etc, but the app is free and you keep books across apps and devices and they're available offline. For example, I brought the NIV in 2001 to read on my Palm Pilot, and was able to use it when I went to Windows CE, and to Android. And my wife can use it on her iPhone.
iOS: http://itunes.com/apps/laridian/pocketbible
Android: https://play.google.com/store/apps/details?id=com.laridian.pocketbible
Website: https://www.laridian.com/default.asp
Apart from that, I also use the Bible App for reading the Bible in Tagalog, since it's not available yet in Pocket Bible. Android: https://play.google.com/store/apps/details?id=com.sirma.mobile.bible.android
PocketBible Bible Study by Laridian, Inc.:
https://play.google.com/store/apps/details?id=com.laridian.pocketbible
I've used it ever since my Palm Pilot days...