Here in Idaho we just signed on to a reciprocal borrowing arrangement. Folks with cards from our library (Pocatello) can borrow from other libraries around the state. The list in the link isn't a list of all the libraries in the state, just the "early adopters." It's a voluntary program but benefits our users, and folks here do travel around!
You'll notice that the Univeristy of Idaho is on the list. Locally, residents of Pocatello can also get "community cards" at the Oboler Library at Idaho State University and, if you join their Friends group (Friends of the Oboler Library, or FOOL) you get even more privileges there.
Many states in the US have such reciprocal borrowing arrangements. (Of course, you have to get the books back to where you borroweds them AND pay any late charges, etc.!) Some agreements, such as that of the Greater Cincinnati Library Consortium, cross state boundaries.