Everyone who has a mobile device should get one of the good, free Bible apps that you can use simply to look up biblical passages and read (or listen to) them. Both Bible.is and the Bible App at YouVersion.com are excellent, simple Bible reading apps that can be used on virtually all kinds of devices. They also have the largest number of versions in languages other than English. If you are a child or have one, check out YouVersion’s Bible App for Kids. If you want to listen to the Bible on your device, most of the apps provide this service, with Bible.is as especially noteworthy.

The other Bible reading apps listed here provide varying degrees of study aids without compromising on simply reading. Since you can use any of these for free, you can try any or all of them and see which one you like best. If you will be using Logos Bible Software (a commercial program with almost unlimited resources for studying the Bible and Christian theology), using the FaithLife Study Bible is a natural choice because it is part of a tightly integrated suite of products. All of these apps have features such as bookmarking, highlighting, and note taking.

Bible.is
http://www.bible.is/
Read the Bible in any of 1,192 languages, or listen to dramatic audio readings in any of hundreds of languages, free. The app is available for iPhone/iPad, Android devices, Kindle Fire, or in a browser.

Bible Gateway
https://www.biblegateway.com/
Read, listen to, look up, and search the Bible in multiple English versions, in Greek and Hebrew, and in other modern languages. The website has a topical index, devotions, reading plans, and more.
https://www.biblegateway.com/app/
The Bible Gateway app, with a free personal account for which you sign up, allows you to highlight and to write and store notes on biblical texts, sync your notes across devices, listen to audio Bibles, and access over 200 different versions in a variety of languages. Can be used on iPad, iPhone, Android phones, and Kindle Fire.

ESV Bible
http://www.esvbible.org/
http://www.esv.org/mobile/
https://www.crossway.org/web-apps/
ESV Bible (online) and ESV Bible App (iPhone, iPad, Android)

The basic app, which is free to anyone who signs up for an account, allows you to sync personal notes, highlights, and bookmarks with ESVBible.org; access the free ESV Global Study Bible; use reading plans; and listen to audio streaming of the Bible. Additional web apps are available for purchase for those wishing to use the app for study as well as reading or listening to the Bible. The ESV Bible for iPhone and iPad and the ESV Bible for Android are also available and can be synced with ESVBible.org.

FaithLife
www.biblia.com
https://faithlifebible.com/
FaithLife is a Christian company with a wide array of resources that integrate with one another, two of which are especially good for Bible reading. Biblia.com is a free online Bible reading website with the Bible available in different languages and editions, a search engine to look for key words, a program called Reftagger that will automatically convert Bible references on a web page you are reading into links to the biblical text, and plugins (Verse for the Day, Bible Search, etc.) that can be put into a web page you have created. FaithLife Study Bible is a free study Bible with the Lexham English Bible. It is designed for use on the web or on mobile devices. Features include personalized highlighting, marking, and notes; three layers of study notes; the Lexham Bible Dictionary (over 2,800 articles); and hundreds of photos, videos, and the like. You can create and join groups (church, school, etc.) and share reading plans, lessons, outlines, notes, and other documents. Free app for Mac/PC, iPhone/iPad, Android phone/tablets, or Kindle Fire. Integrates with FaithLife’s other programs and resources, most notably Logos Bible Software.

Olive Tree Bible Software
https://www.olivetree.com/
App for Windows, Mac, iPad/iPhone, Android, and Kindle Fire; sync to all devices. Over 100 free books include several English versions (ASV, ESV, HCSB, JPS 1917, KJV, NET, NIV, NKJV, RV, and more), Greek NT texts (Byzantine, Scrivener, and SBL), the Leningrad Codex Hebrew Bible, the Vulgate, and a few older commentaries (Henry, Jamieson-Fausset-Brown). Compare texts or versions side by side, take notes, highlight and bookmark verses, and choose a reading plan. For those wishing to use the program for study, you can consult your reference library, for which you can purchase additional resources (translations, study Bibles, versions, commentaries, maps, study tools, etc.) if you choose.

Wave Study Bible
http://www.wavestudybible.com/pages/bibleapp/index.html
Despite the name, the Wave Study Bible is essentially a nice, simple Bible reading app for the iPhone and iPad that compares three translations (the KJV, arranged side by side from literal to paraphrase. You can find verses in four different ways, including a search wheel and a search slider. The app is free; additional translations are available for purchase.

YouVersion
https://www.youversion.com/
The Bible App and the Bible App for Kids. More than 1,200 versions in over 900 languages, with many audio Bibles. Available on pretty much every kind of device. Highlight or bookmark verses, attach public or private notes. Reading plans, and devotionals. Subscribe to verse of the day. Some Bible videos as well. All free, no in-app purchases. Installed on well over 200 million devices.

See also: 

Choosing a Good Study Bible

Free Bible Study Apps and Programs

Professional Biblical Studies Software Programs