A new collection from the Library of Congress. The Traditional Music and Spoken Word Catalog is a searchable database that includes information on musical recordings; most of those covered are from 1933-1950.
This database is just one collection in the Music Theater and Dance Performing Arts Digital Library which showcases important artistic documents and materials related to American culture.
The main site even offers an "Ask a librarian" service, to help you explore the collection.
Another collection is on Amazing Grace, and includes recordings and hymnals.