TheStatutoryApe said:
The first thing to come to mind was World of Goo but it has been mentioned several times already. I have not played it myself but I would love to I just don't have a Wii.
This is available on the PC, and a GREAT game. Similar style games: Osmos, Solar 2.
As mentioned many times, the Portal games are amazing. If you haven't played them, you are missing out on a significant moment in gaming history.
Spore (must), Anno 1404 (must), Tropico, Startopia, Children of the Nile... all of these games have the option to fight, but you can have just as much (probably more) fun just building up your empire and trying to manage it. Staying ahead of the curve and keeping your population happy and thriving can be a real challenge and makes you approach gaming in an entirely new way. I never really liked Sim-city, but there's also that...
I'm not sure if the OP's getting tired of violence per se, or just the glut of games that spew an endless stream of baddies at you, blocking your path to the NEXT level and offer little more than "shoot shoot kill kill!" There are quite a few games that are violent, but have so much depth that you get lost in the game, and don't really feel like the whole point is just killing stuff -- you can spend hours on end doing other things when you aren't in the mood for violence. Some examples would be Fallout 3, and Oblivion - both a must if you've never tried them.
Most RTS games are essentially about war (as is chess), but there are a few where strategy really comes to the front, and the violence itself gets sublimated, e.g., Bungie's Myth and Homeworld 1 & 2. Not an RTS, but a great strategy game - Defense Grid the Awakening.
I'm to the point where I have a hard time playing most FPS games these days - most of it just seems like mindless target practice with a thin story added after the fact. However there have been a few that hook me even though they are violent, simply because the story or the gameplay is so engaging: Batman Arkham Asylum, or The Witcher, or Tron 2.0 (NOT Tron evolution). The violence seems secondary, and not the whole point of the game.
Anyway, I know I've strayed a bit from "no violence at all." Hope this helps you find something that isn't just "shoot kill shoot kill."