If you have an Amazon Prime membership, you can check out a book a month on your Kindle without paying anything extra. The problem is it’s really hard to search for which Kindle books are part of the program.
Here’s a link to an Amazon search result that will show you all the Prime eligible books:
You can also get to this page by going to Amazon, searching in books and checking the “Prime  Eligible” box but half the time the box doesn’t show up for me and I can’t click it, so I just bookmarked the link.
Now I just wish you could check out more than one a month …
Disclaimer: my affiliate code is in the link above so I will get a referral fee if you buy a book using that link.