On unless I need to be quiet! Then off. I especially need sound effects to alert me to stuff so I'll increase the vol on the SFX but decrease the music a tad (if these fine tuning options are available).
I keep the music on for 90% of the games I play. Some of the animal crossing NH hourly music is ghastly to me so that's when I turn it off. I wish we could have a setting where we hear surrounding sounds (water, footsteps) but not the music.
I always keep the music on unless I'm just like grinding away at something and thus have something else playing in the background. After all, the music is part of the game and I need to listen to it to get the most enjoyment out of my games.
Usually on! The SFX and music of a game play a big role in my enjoyment. If I'm doing something like decorating in Animal Crossing for hours, though, where immersion isn't my first priority, I might mute and have my own music on. I can only listen to the hourly tunes for so long haha.
I personally leave the music on for most games I play, and when it comes to games like AC, SDV and Mario Kart I actually find it disorientating to NOT have the music on.