Voted #4.
It's variable. It depends if I like the soundtrack or not, to start with. If it's good, I usually leave it on, but the volume will usually not be turned all the way up to max. Even if I love the soundtrack I'll usually keep it at maybe half volume since I do prefer to hear the rest of the game's audio in priority over the music. But there's been some exceptions to that 'rule'. In cases where the "music" is actually more of an ambient soundtrack and isn't too melodic then I can in those specific cases just leave it on at full volume if it doesn't bother me much.
I've done that for a few games such as STALKER (the first one) and both Borderlands 1 and 2. However, even in those cases sometimes the music will be dymanic and based on what's happening (I.E. exploration music, or combat music) such as the soundtrack of the Elder Scrolls games. That's where mods come into play, where I would leave the exploration / outdoor music play at around full volume most of the time, but would mod the game in order for the combat music to be turned almost all the way down or simply turned off (or specific combat tracks to be removed, but keeping some at half volume).
Now, in cases where I like the game but don't like the music much I'll usually just turn it off and play something else in the background from the desktop apps, or I'll just plain and simple play without music at all. I've done exactly just that for Diablo 3 for the majority of the years I've played it. I don't "hate" D3's OST, but I simply don't like it enough to keep it on all the time. I've heard it play a couple of times and it was enough (D2's OST was a completely different story though; kept it on all the time at near max volume).
So yeah it's variable and pretty much a per-title case by case scenario.