A list of national libraries is maintained on Wikipedia by the International Federation of Library Associations and Institutions (IFLA).
UNM's reference librarians and subject specialists can also help you identify libraries useful for your particular research in different countries.
Library cultures and access policies differ greatly around the world.
Many libraries, including many of the major libraries of Europe, have closed stacks (i.e., you won't be able to browse the books on the shelves). They may also have limited hours of operation and may charge access fees. Count on needing to plan ahead, and plan your research time carefully.
Some libraries require a letter of introduction from a librarian just to use the facility. We're happy to provide these letters; just let us know when and where you're going. You may also ask us to help identify libraries useful for your particular research.