It's hard to get good books for free in the kindle store. If there are any, they'd be older books and classics and such. What about looking into your nearest public library?
Well, first, beauty is in the eye of the beholder. What kinds of books do you like? Sci-fi? Mysteries? History? That will help us make recommendations. Second, google free kindle books. I get 3 or 4 emails a day with a list of free or discounted books. Most of them are only good for the day that I receive them. Good luck!
Jaja dont limit yourself to the kindle store You can download books as PDF files and then search up pdf to kindle files on google and that will take you to an online converter that works very well. I would recomend games of thrones (and the rest of the series) and I recently read Fall of the Giants by Ken Follet and it was very good (its historical fiction, some people may no really be into this kind of stuff)
I usually go into the Teen and Young Adult Categories that have romance books, mystery books, horror books, and sometimes I like fantasy.
I was just going to mention the free Kindle store. On there I found Deployed by Mel Odom. I'm a military aficionado so it was awesome for me, but some people had trouble handling just how graphic and serious it was at points. EDIT: I tried searching and I'm not sure if it's free anymore But it was still great for anyone who's up for an intense and yet really touching story of an earnest military mom.
The Knife of Never Letting Go is a book that I enjoyed very much as a teenager. It has a little bit of sci-fi, but it doesn't pop up very often. It's mostly a thriller book. I doubt it's free though.