Video

Stanford connections

Christopher Costanza performs the cello suites of Johann Sebastian Bach
Robert Huw Morgan performs the complete organ works of Johann Sebastian Bach
Riverwalk Jazz - streaming jazz and blues radio programs
St. Lawrence String Quartet Youtube channel, featuring Haydn

Sounds from Europe and the USA:

All of Bach (Bach from the Netherlands. a new performance each week, forever!)
Europeana Sounds (Sounds from museums, archives and libraries throughout Europe)
Opera Platform (free streaming operas, launched in 2015)
Steinway Streaming (lots of piano, of course!)

Historical music recordings

Internet Archive Great 78 Project (68,000+ discs!)
The National Jukebox (Library of Congress--see all online sound recording collections at the Library of Congress)
The Cylinder Digitization and Preservation Project (University of California, Santa Barbara)
Belfer Cylinders (Syracuse University)
The Virtual Gramophone (National Library of Canada)
La Phonobase (in French)
Stradivari Quartet/Iowa String Quartet (University of Iowa)

Downloads for sampling, mashing, podcasting

BBC Sound Effects
Free Music Archive
CC mixter
Jamendo
Free Sound Effects

Spoken words

American Leaders Speak (recordings from World War 1 and the 1920 election at the Library of Congress)
U.S. History Out Loud
Supreme Court of the United States Audio Archives
The Poetry Archive
Internet Poetry Archive (University of North Carolina)

Also of interest

Historic Naval Sound & Video
Bug Bytes (digitized insect sounds)
Macaulay Library audio archive of biodiversity
Internet Archive - Audio Archive
Western Soundscape Archive (field recording archive)
Every Noise at Once (Algrhythmically-generated samples presented in a scatter chart; built on Spotify.  See also other charts in the footer)
Music Animation Machine (beautiful real-time visualizations of musical works)