Been ninja'd on some of these, but...
- The entire city-building genre (except the ones with wargame elements like Caesar)
- The realistic simulation genre, games like Flight Simulator and RailWorks (including The Sims, which acts the part)
- Sports games...well, unless you think sports are violent. I suppose football and hockey dance around the line, but baseball, soccer, and basketball aren't violent sports.
- Puzzle games, as a general rule. Exceptions include Puzzle Quest and Portal.
- The tycoon genre, again, most of the time. Some tycoon-type games have light wargame elements (the Patrician/Port Royale series).
The above constitutes about 95% of my game collection. Really, except for Grand Theft Auto and Bethesda Game Studios' body of work, I don't play many traditionally-violent games.