Please feel free to add to this.  I would love to see other suggestions posted here.  :-)

1. Dollar Tree -  I have found some absolutely adorable books at the Dollar Tree. Just recently, I found 4 that were paperbacks & have the cutest storylines.  What a great deal!!  You can't beat getting a brand new, cute storyline book for a buck!
2. Ollies Bargain Outlet - I realize that Ollies isn't in all states, but if you happen to have an Ollies, they often have wonderful children's books as well as other educational things to teach children.
3. Salvation Army (& other thrift stores) - I have found some awesome books by perusing my local Sal's.  Usually though, they are all mixed together & you will need to take some time to look through everything.  Also, since they are used, you will have to look the books over to make sure they are in good shape.  I got the Barnyard Dance by Sandra Boynton (Big Board Book) from there for $1 & it looked brand new!).
4. I recently was in Manassas, VA.  If you live there or anywhere near a McKay's Used Bookstore, they have an awesome selection.  I got some hard back children's books in beautiful shape for $.75!  I think their stores are mainly in Tennessee & Virginia.
5. Local library sales.  I have also found some great sales through my local library, but again, you have to look the books over to make sure they are in great shape.
6. Of course, last, but not least - PBS!  :-)  I have gotten a wonderful selection of books through PBS.  Thanks, PBS.  You are the best!!

Anyone?

ITA about Ollies and the others you have listed. I have never walked out of Ollies without buying at least 3 books. McKays is amazing, but the only time I ever get to go is when we drive through TN to visit my sister in Atlanta, which is once a year at best. Other places I've found great children's books are Half Price Books and Big Lots.