Not the End, specifically taylored to stir the story towards dramatic conclusions for the characters, without any combat needed. (Generic engine.)
Brindlewood Bay for who-dunnits in which combat is not really supposed to happen (the characters are old female amateur detectives).
City of Mist for noir investigation, where combat, though entirely possible, is treated exaclty as all the other things you can do (no subsystems). (Legend in the Mist is kinda in the same bracket, system wise, but decidly geared towards adventure.) I played more than one hundred sessions with this one, with two "combats", total.
Night Witches, or any other opinionated PbtA out there without any focus on "adventures". (In Night Witches you play as female pilots in the soviet army during WWII. The focus is decidly not combat, even if there are some aerial fight scenes.)
Fiasco, where there isn't any system for action resolution — only scene outcomes.
Nephilim, for occult mysteries, decidedly not geared towards combat (mechanized through the basic system in its first iterations, now quite far from its roots). You play as mythical creatures reincarnated in human bodies through countless generations, searching for answers in your mystical quests.
Lot of others that don't come to mind right now.