I suppose this entirely depends on how violent you consider "violent," as sad as that is.
Rhythm games might suit your fancy. Audiosurf, Guitar Hero, Stepmania, etc are good fun without violence. I've spent months of time total on Rollercoaster Tycoon, although you might be hard-pressed to find a copy of any version nowadays. 2 is the best, and dammit I'm going to reinstall it now that I'm thinking about it.
Terraria and Minecraft are good fun if you're into exploring and creating stuff, though there is pixelated combat and stuff reminiscent of an SNES game but with a much larger screen and, in the case of Minecraft, a 3d view. Do any search for Terraria or Minecraft and you'll see how they look.
Plants VS Zombies is silly, there's really no other word for it. You've got a bunch of plants warding off zombies by shooting peas, blowing up hot peppers, tossing watermelons at them, and all kinds of stuff. PopCap has a lot of non-violent games that might be worth looking at. Just don't get hooked on their facebook crap by sinking money into it.
Worms is also a silly one, though definitely more violent, but it might be acceptable. You have a bunch of cartoon worms that pretty much try to kill each other with various cartoony weapons, some based on real weapons like the shotgun and others that are more fanciful like the holy hand grenade or concrete donkey. The only blood in it is if you turn it on, and then it's more like a splat than anything else. Worms: Reloaded is the latest and available on Steam.
What consoles do you have, if any?