Music used in streams and videos
When a game does not have custom music, these are the playlists usually used for streams.
You can use the command !song in Twitch chat during stream to check which song is being played. (Of course this doesn't show the correct info for in-game music.)
Minecraft Music
Mojang Studios - Link to Spotify
C418 - Link to Spotify
Lena Raine - Link to Spotify
Gareth Coker - Link to Spotify
Henzoid - Link to Spotify
Music from Minecraft events
The songs of these events have been collected in one big playlist.
Klyx Games - Link to Spotify
MCC - Link to Spotify
Crown Quest - Link to YouTube
Cube Championships - Link to Spotify
BlockWars - Link to Spotify
Solar Skirmish - Link to Spotify
Pandora's Box - Link to Spotify
Fusion Frenzy - Link to Spotify
Fruitwars - Link to YouTube
Knights of the Square table - Link to Spotify
Other
PGN Music - Link to Spotify
Wintergatan - Link to Spotify
Total Mayhem Games - Link to Spotify
Taiji - Link to Spotify
YouTube
For YouTube videos, music is mostly picked from this playlists, and features:
Mojang Studios - Link to Spotify
C418 - Link to Spotify
Lena Raine - Link to Spotify
Gareth Coker - Link to Spotify