Yes, you can download only one Prime book/month.
However, if you go to Amazon, Shop by Department, Books, Kindle Books, you can choose the type of book for which you're looking from the menu on the left. After selecting this, sort by price, low to high, and there are multitudes of books you can download for free with an Amazon account. I sometimes get up to 30 books/day doing this. Some are AZ3 file times, but some are MOBI. You can send them directly to your device, download them to your computer to transfer to your device, or get them in the archives on Kindle for PC.
I find that reading some of the not too familiar authors is refreshing, and you find some gems out there that are certainly worth the free download.