To be perfectly honest, after using my sister's, I almost considered buying one solely based on the fact that I wouldn't have to fight with the binding of a book.
Aside from that, being able to browse and purchase books from anywhere is definitely convenient, as well as having any book you want at your disposable without having to plan/store/carry copies of said books ahead of time.
"Kindle makes it easy to search within a book, across your library, in the Kindle Store, or even the Web. To use the Search feature, simply type in a word or phrase you're looking for, and Kindle finds every instance in your book or across your Kindle library. Looking for the first reference of a character in your book? Simply type in the name and search. You can extend your search to the Kindle Store to find related titles you may be interested in. Explore even further by searching Wikipedia and the Web."
Aside from that, being able to browse and purchase books from anywhere is definitely convenient, as well as having any book you want at your disposable without having to plan/store/carry copies of said books ahead of time.