I'm writing this entry because I looked for this answer recently, and couldn't find what I needed. Can you read Kindle books on a Nook? Well, online information I found said, "No."
Those sites, thankfully, are wrong!
The Nook HD+, which is the top of the line Nook tablet and e-reader, comes with Google Play, which means that users can install Google Play apps.
So, if you have an Nook HD+, make sure the firmware and software are updated to the latest versions. Then open Google Play, and click the Apps button. From there, you can search for Kindle, and the Amazon Kindle app will come right up.
I frequent Barnes & Noble often, and really like the Nook HD+. Also, they've been on sale for a huge discount lately. My parents got me one for my birthday (thanks Mom and Dad!). I had heard that there was a Kindle app for Nook from a friend, and since I already have a ton of Kindle books, I was excited about that feature.
I didn't guess the Google Play angle myself. My friend told me to check there, so thank you, Crystal! Now I can read everything in my large Kindle library, as well as my new Nook titles.