I donate my used/read paperbacks to my local library all the time. When I get a paper grocery sack full, I drop them off. No issues. They either recycle or sell - their choice. I usually rent from my local library (in hard/soft cover vs electronic) and only buy when I am out of town and out of a book or locally when I am out of a book and the library is closed.
The local library is such a valuable resource that, sadly, most folks just don't realize. In addition to reading material there are tons of resource materials; cultural event tickets; etc. I love libraries and 'real' books!