List of national libraries is maintained on Wikipedia by the International Federation of Library Associations and Institutions (IFLA)
Libdex: The Library Index is an extensive list of library web-based catalogs and home pages.
Cornell's reference librarians and subject specialists can help you identify libraries useful for your particular research.
Library cultures and access policies differ greatly around the world.
Many libraries, including many of the major libraries of Europe, are closed stack (that is, you won't be able to browse the books on the shelves). They may also have very 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.
There are Cornell librarians with expertise in collections and services related to particular world areas.
Who are the specialists for your disciplines and destinations? Find out by consulting this list of Cornell Library Subject Librarians.
Abbey Library of Saint Gall, Switzerland; credit: clare_and_ben, Flickr, Creative Commons license.