Facsimiles on the Worldwide Web
British Library
DIAMM
IMSLP.org
Library of Congress
Loeb Music Library
The Morgan Library & Museum
National Library of Austria
In OneSearch, after limiting to "Library Catalog" and "Music Collection" as the Library Location, You can add specific keywords to find primary sources in the collection, for example:
facsimile -- for reproductions of original handwritten manuscripts or early printed music
correspondence -- the Library of Congress subject for letters of specific people is "correspondence."
interview -- many composers and performers have been interviewed by members of the popular press and by scholars.
There are several collections of primary source reading excerpts (translated into English) for music history:
Source Readings in Music History, 2nd edition, by Oliver W. Strunk and Leo Treitler
Music in the Western World: A History in Documents, by Piero Weiss and Richard Taruskin
Music through Sources and Documents, by Ruth Halle Rowen
Source Readings with a Topical Focus:
Jazz:
Keeping Time: Readings in Jazz History, 2nd ed., by Robert Walser
Reading Jazz, by David Meltzer
Reading Jazz: A Gathering of Autobiography, Reportage, and Criticism from 1919 to Now
Music Education:
Music Education: Source Readings from Ancient Greece to Today, 4th ed., by Michael L. Mark
American Music
Music in the U.S.A.: A Documentary Companion, by Judith Tick and Paul Beaudoin
Readings in Black American Music, by Eileen Southern
Music Theory and Philosophy:
Contemplating Music: Source Readings in the Aesthetics of Music, by Carl Dahlhaus and Ruth Katz
Music in European Thought, 1851-1912, by Bojan Buic
The Routledge Companion to Philosophy and Music
Other Collections of Source Readings:
Audio Culture: Readings in Modern Music, by Christoph Cox and Daniel Warner
Greek Musical Writings, by Andrew Barker
Modernism and Music: An Anthology of Sources, by Daniel Albright
Readings in the History of Music In Performance, by Carol MacClintock
The Routledge Reader on the Sociology of Music, by John Shepherd and Kyle Devine
Women in Music: An Anthology of Source Readings from the Middle Ages to the Present, by Carol Neuls-Bates.