Besides countless VNs, Point, Click Adventure games, puzzle games, building games, such as SimCity, Rome and Anno, though the latter two have combat, or simulators, such as EuroTruck Simulator or Microsoft Flight Simulator, though the latter two categories aren't character oriented, there are games with minimal combat that don't fall into these categories.
The Guild 2, is a merchant simulator set in the Reinasance, and you can go into politics and set the guards on your adversaries, hire people to burn down your competitor's shops and homes, marry your waifu and raise a happy family, go to church, avoid the plague, and you could just be a lowly businessman who has a bakery and sells bread every day. The choice is yours.
There are also plat formers that barely have any enemies and the objective is just to avoid the obstacles, such as DustForce or SuperMeatBoy.
Age of Decadance, is an RPG, that from what I heard can be plaid without engaging in combat.
Thief 1&2 are more about stealing stuff, than it is about fighting, at the hardest difficulty you loose the mission if you kill guards or civilians.
There are also plenty of porn games, but you are better of asking /hgg/ about that.
Most sport series like, FIFA, Tony Hawks Pro Skater and racing series such as Need For Speed and Burnout, don't have "combat" do you do compete against other players, with the exception of Tony Hawk, since that is more about having a high score.
So you have plenty of games to choose from.