Can I read non-Amazon books on my Kindle?

I got a Kindle for Christmas and I love it. It’s been very fun and I’m pretty happy with the Kindle Store. But, I just got an email from Barnes and Noble offering 15% off e-books. I can’t find a solid answer for this question, so I thought I’d see if anyone here has had success. If so, how did you deliver the book to your Kindle?