Harvard College Library has a Science Fiction Collection in the Houghton Library that has over 3,000 volumes of “trade paperbacks, magazines, fanzines, and prozines.”
The University of California, Riverside is home of the Eaton Collection of Science Fiction and Fantasy. It claims to be the largest publicly accessible collection of science fiction, fantasy, horror, and utopian literature in the world. It has over 300,000 items, including fanzines, pulp magazines, comics, hardback and paperback books, and various collectibles.
This is also the home of the Eaton Journal of Archival Research in Science Fiction. The folks at Eaton Journal have created a Google map of science fiction archives throughout the world.
The University of Iowa Library is the home of the M. Horvat Collection of Science Fiction Fanzines. This collections houses 15,000-20,000 items from 1925 to 2002 (with most items from the 1960s to 1980s).
The University of Iowa is also home to the James L. “Rusty” Hevelin Collection of Pulps, Fanzines, and Science Fiction Books. The university is working on digitizing the collection. They are charting their progress on tumblr.
Georgia Tech also has a science fiction collection that holds more than 10,000 science fiction and fantasy novels, as well as many periodicals.
The Cushing Library at Texas A&M University is the home of the Science Fiction and Fantasy Research Collection, which holds monographs, periodicals, and manuscripts, and has over 20,000 titles.
Virginia Polytechnic Institute and State University is home to the William J. Heron Collection of Speculative Fiction.
Cal State Fullerton’s Special Collections has a science fiction collection that includes, among other things, original manuscripts and related materials of Philip K. Dick and Frank Herbert.
The Internet Archive has a Pulp Magazine Archive that contains almost 5,000 items. Lots of cool stuff to browse online.
Museums and Exhibits
The National Museum of American History (part of the Smithsonian) currently has an exhibit called Fantastic Worlds: Science and Fiction 1780-1910.
Two museums of science fiction are in the planning and fundraising process: the Museum of Science Fiction (to be house in Washington, D.C.) and the Hollywood Sci-Fi Museum (to be located in Hollywood, CA).