The Kindle app gives you access to Amazon's extensive ecosystem of over 1 million e-books. There are plenty of magazines, newspapers, and textbooks as well, and the app will keep track of your place when you're reading, making it easy to switch between devices. If you're an Amazon Prime member, you'll get access to Kindle's Lending Library, which lets you borrow one book at a time from a selection of titles, and there's always Kindle Unlimited if you want a Netflix-esque service, but for books.
Price: Free (iOS, Android, Windows Phone)