I really do love them!
So, here are some more ways to get free books.
My kids each get a book from Dolly Parton each month through her Imagination Library. This program is not available in all areas, but it is worth checking! If it is available in your area you can sign up your child if they are between birth and age 5. Then a books is sent to you each month. We have gotten a couple of repeats with the second child, but they switch them up frequently. (Thanks to Amy for reminding me about this!)
Review books for a publisher. Usually all you need is a blog, which are so easy to set up if you do not already have one. I review for several Christian publishers, but I would suspect secular publishers would have similar programs. Search their websites for 'book review' or 'media requests'.
Garage sales and thrift stores are not free, but they are inexpensive and have many undiscovered treasures. You can get a steal on a book that has barely been read.