Library of Congress (LC), Local History and Genealogy Reading Room. This part of the Library of Congress in Washington, DC, includes 50,000 genealogies, 100,000 local histories, manuscripts, microfilms, maps, newspapers, photographs, and books. It is strong in North American, British Isles, and German sources. See the website at http://www.loc.gov/rr/genealogy/ and the FamilySearch Wiki article at https://wiki.familysearch.org/en/Library_of_Congress.
National Archives and Records Administration (NARA). The NARA, located in Washington, DC, has census records, pre-WW1 military service and pensions, passenger lists, naturalizations, passports, federal bounty land, homesteads, bankruptcy, ethnic sources, and prison records. See the Wiki article at https://wiki.familysearch.org/en/National_Archives_and_Records_Administr.... The NARA also has about a dozen regional centers. For locations, see http://www.archives.gov/locations/archival-research.html.
Family History Library (FHL). The Family History Library in Salt Lake City has 450 computers, 3.1 million microforms, 4,500 periodicals, 310,000 books, and a collection of microfilmed records such as civil, church, immigration, ethnic, military, and Mormon records. See the Wiki article at https://wiki.familysearch.org/en/Family_History_Library. The library has over 4500 branches called family history centers located worldwide. Search for a center at http://www.familysearch.org/eng/library/FHC/frameset_fhc.asp
Allen County Public Library (ACPL). The Allen County Public Library in Ft. Wayne, Indiana has a premier periodical collection, genealogies, local histories, databases, military, censuses, directories, passenger lists, ethnic collections, Canadian, British, and German collections. It is the home of the Periodical Source Index (PERSI). See the Wiki articles at https://wiki.familysearch.org/en/Allen_County_Public_Library and https://wiki.familysearch.org/en/Periodical_Source_Index_(PERSI)
New York Public Library (NYPL). The Genealogy Division of the library has an outstanding collection of American history, international genealogy and heraldry, the Dorot Jewish collection, photos, and New York censuses, directories, and vital records. See the Wiki article at https://wiki.familysearch.org/en/New_York_Public_Library
New England History Genealogical Society (NEHGS). The society, located in Boston but national in scope, includes a 100 million name database, vital records, genealogies, journals, over 200,000 books, 100,000 microfilms, and over 20 million manuscripts, with emphasis on New England and New York since the 1600s. See the Wiki article at https://wiki.familysearch.org/en/New_England_Historic_Genealogical_Society.
Mid-Continent Public Library, Midwest Genealogy Center. This library in Independence, Missouri, contains national censuses and indexes, 80,000 family histories, 100,000 local histories, 565,000 microfilms, 7,000 maps, and newspapers. See the Wiki article at https://wiki.familysearch.org/en/Mid-Continent_Public_Library_Midwest_Ge...
Dallas Public Central Library. This library has 111,700 volumes, 64,500 microfilms, 89,000 microfiche, and over 700 maps. It includes state and county marriage, probate, deed, and tax abstracts in book form and microfilm of originals for some states, and online databases. See the Wiki article at https://wiki.familysearch.org/en/Dallas_Public_Central_Library
Newberry Library. The Newberry Library, located in Chicago, has genealogies, local histories, censuses, military, land, indexes, vital records, court, and tax records mostly from the Mississippi Valley, eastern seaboard, Canada, and British Isles. See the website at http://www.newberry.org/genealogy/overview.html
Sutro Library. This library, located in San Francisco, has 150,000 books, 65,000 microforms, 40,000 state, county, or town histories, 10,000 genealogies, rare books and manuscripts, indexes, guides, and databases on genealogy and California history. See the website at http://www.library.ca.gov/collections/#sutro