Libraries tend not to have genealogical records or data, but they can be an excellent source of information and history about the area, maps, photographs, etc.
Directory of Genealogical Libraries in the US – Hundreds listed by state with contact information, many with hot links
Allen County (Ft. Wayne, IN) Public Library – Extensive collection of resources and databases for Indiana and the Midwest
Library of Congress – European Reading Room
Library of Congress – Polish Directories
Newberry Library – Chicago
Polish Museum of America Library – Chicago
Polish Library – London