Zoo Tycoon 1-2 (there can be violence, but it's not the goal and considered bad).
Rollar Coaster Tycoon 1-3 (Same as above).
Most sports games
Undertale, if you play as a pacifist
Feral Heart (Not really a game though, it's more like an advanced chatroom where you are an animal.)
Cereal Soup (same as above, but it's unfished and they will add hunting.)
Might count as violence:
Spore, if you play as a pacifist (but there might be some near the end even then... I really only use the creature creator.)
Lethal League (like an aggressive game of dodgeball. Probably the most violent on this list, but no blood or death.)
I also heard you can play as a pacifist in Fallout 3-4 but I haven't played those.
The only one I have played recently is Lethal League, so this might be off a bit. I also recently tried to do a pacifist playthrough of Skyrim. I managed to complete the main questline with only two kills, but it was hard and frustrating.
· 5 months ago