I know you mean libraries. But there are several Netflix for books.
BookSwim
BooksFree
BookSpine
I have a friend who is a member of one of them (can't remember which) and likes it quite a bit. Not because she doesn't realize libraries exist but because of the Netflix-like queue, never having to wait months for a current bestseller to be available while waiting through a 200 person hold backlog, and having to schedule trips to the library in the relatively small windows when they're open and she's not at work.