A game that has absolutely no violence... *shutters* i mean hell, even basic point and click adventures usually have some violence somewhere (Machinarium uses low level violence throughout it) I guess racing games could be classified as non-volent, Osmos (if you look at it right), but actual full (decent selling games) that have no volence anywhere, dam near impossible, hell, the sims even allow violence (kill your sim, lay waste to you city), flight simulators you can crash.. basic violence/damage to yourself/others/property is a part of everything, if a game doesnt have it, it lacks conflict, lacks story, and you would have trouble classifying it as a game, the answer to you question would depend entirely on how strict a definition you use, the strictist definition will return 0 games simply because almost any action can be viewed as violence towards something, and without it, how do you loose.
Puzzle games being the exception as long as you dont take a, sorry, ****ing stupid outlook on them.
Oh, and i love war/fps games with exceptions (Osmos was a great game)
YAY rant!
