Kindle for iOS is an excellent e-reader app that seamlessly ties to your Amazon account. The latest version comes with new book samples that let you read the first chapter of any book before buying, and lets you download third-party dictionary apps for looking up definitions while you read.
Unfortunately, Apple's stringent App Store rules against apps that compete with iBooks mean you'll still need to buy books through Amazon's Web site instead of from a dedicated e-book store within the Kindle app. Luckily, the process is pretty easy once you get the hang of it, and you can download the first chapter for free.
Obviously, the workarounds don't make for an ideal user experience, but it's also not too much trouble, and having the power of both iBooks and Amazon is worth learning the process. The Kindle app also comes with a few bells and whistles to enhance your overall mobile reading experience.
The app opens up to the Home screen, which is entirely blank on first launch, with no best-seller lists, and other curated content like you would find in iBooks or Kindle on other devices. The Home screen will not be blank if you have books already tied to your Amazon account, and you can select to view the covers as thumbnails or in a list. From here, you can either tap a book to go inside or long-press to delete it from your library. Across the top you have buttons to sort by all your items, just books, your newsstand, or the docs you have saved to the Amazon cloud.
Like I said above, if you want to expand your library, the best way is to use your Web browser then transfer the books to your iOS device. However, you can touch a magnifying glass in the upper left that lets you search for books and -- in this latest version -- download a sample that has roundabout purchase options at the end. Along with books, magazines, and newspapers, the Kindle app offers illustrated children's books, comics, and graphic novels. All let you preview the first chapter of any book before buying.