This essential list was put together by Jane Little for TeleRead. Little actually created a much larger list of must-have iPad apps for readers, I just took the 7 that are free, which also happen to be the best.
Kindle App—this app reads mobi or prc books, but unecrypted only. Another unecrypted mobi app is eBookMobi.
Nook App—download this ONLY if you are a BN reader
Bluefire App—this is the best ePub reader out there if only because it allows you to use library downloads but also because you can add ePubs via sideloading or via dropbox/email. The Nook App does not allow this. Overdrive is another good library reading app. If you have a Kobo, you will want the Kobo app which accepts unencrypted epubs. Read more about how to use the Bluefire App here.
Dropbox—allows you to always have easy access to your ebooks. You can add your encrypted ePubs, your unencrypted ePubs, Mobipocket, PRC, PDFs into the dropbox folder and then access it from your iPhone or iPad so long as you have an internet connection. This way you don’t have to plugin your iPad and do a tedious sync to get one book on your iPad.
Instapaper—using a Bookmarklet (a bookmark for your webbrowser that contains a small script), you save all these articles to read later, rather than continuously email them to yourself. It allows you to read all articles in one place.
Evernote--use it to write notes to yourself but you could use it save lists of books you want to buy. It saves your work (automatically) and then syncs it so what you have on your computer is exactly the same as what is on your iPad.
Audible—the Audible App is designed for the iPhone only but it is useable on the iPad. From within the Audible App, you can download your purchases without syncing to iTunes. You can’t purchase directly from within the app, instead, like the other apps, a purchasing link launches Safari.