Can be from any genre. Mine is when an acoustic guitar comes in towards the end of a song and totally changes or reframes the mood/energy (see "Money" by Widowspeak)
Not sure if this is a trope per se, but I love when sounds don't sound "perfect" - the producer kept in a little vocal waver, or the snare isn't hit with the exact same intensity every time. The little imperfections make it feel/sound like real humans are playing the music!
I think that can be said about pretty much any creative work. Those little imperfections are what make it real, and I love it.
Hollywood using old vintage lenses for their design flaws, CG artists deliberately putting scratches and dust spots on their models, and so many more examples.
To come back to music, I believe no robot will ever be able to play Clair de Lune with the gentle delicacy and softness that a human who just lets themselves flow with the sound can produce.