This is a list of ones I've had recommended to me or have used myself. I'll try to keep it updated if people let me know of ones they find helpful and why. Links are to the Google Play store; I'm sure most of these exist for Apple devices as well.
- The Bible App from Life.church
- One of the best apps for "just reading" the Bible. It has lots of translations - I'd recommend the UK edition of the NIV, or the New Living Translation. It also has a variety of reading plans with notes, but they tend to be quite short and I've not really used them.
- Olive Tree NIV Bible
- This is a proper study Bible, with maps, commentaries, etc. (often via in-app purchases), as well as several translations and reading plans.
- Blue Letter Bible
- This is more useful for the Bible geeks, as it lets you read the English in parallel with the Greek or Hebrew if that's your thing. The best translation on there is probably the HCSB, which is pretty good.
- Bible in One Year
- HTB's app for helping people read the Bible in a year, complete with notes from the staff at HTB. Note - Bible in one year is about 4 chapters per day, so expect a fair bit of reading!
- Daily Prayer
- The official Common Worship Daily Prayer app, for those who like things a bit more traditional but still on their phone. It gives you a short service of Morning Prayer, Evening Prayer and Compline every day, with the readings and prayers changing with the dates and seasons.
- PrayerMate
- OK, not actually a Bible reading app, but it's great for managing lists of things to pray for and giving you reminders to pray!
