The Civilization series. You *can* win the game through imperialism, but you can also do so through diplomacy and other non-violent means.
Oh and:
It's like Wolfenstein 3D with sheep in place of SS guards and you put them to sleep with food that you shoot from a slingshot.
Chess imho
Edit: Almost forgot, twirling your thumbs yeah
Some of my fav none violent games
Roller coaster tycoon series
Harvest Moon
Farm simulator
Farmville
The Sims
Sim city
Flight Simulator
Anon 2070
Spore ( you can goo all the way to the end with zero violence if you REALLY try )
Mario and Tetris come to mind. As well as a shit ton of sports games. Pending on what you consider violence...you might not even be able to have games like zelda or metroid on this list. But that's just silly to me, I don't consider those games violent.
Ooooh and Sonic the Hedgehog
mario is a mass murdering game, those poor turtles =(
Dishonored can be violent or it can not be. It's actually a harder game non-lethal but you're rewarded if you never kill anyone.
Lemmings
10chars
You beat me to it
What do you mean by violence? Amount of blood and gore coming out during killing process? Or necessity to kill anything in game in general?
Even in Sims 1 you could "occasionally" (I did on purpose for the lulz) burn the kitchen together with sim, or send sim to water bath and forget about him. Then house would become haunted, and ghosts of sims would torture the living during night. How is it not violent?Some of my fav none violent games
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The Sims
Sim city
Sim City involves playing with tax system, has options to summon Godzilla and various catastrophes on your city, taking away millions of innocent lives. How is it not violent?