- Civilization IV //PC, Mac. Technically, you can go to war with other nations, but that's only a small aspect.
- Glider Pro //PC, Mac. A very simple game, but actually sort of significant historically in the development of Mac gaming.
- Uplink: Hacker Elite //I've only played the demo, but it's pretty cool.
- Sky Odyssey //PS2. If you got one, and you are open towards flight games, then Sky Odyssey is a pretty good bet, despite the N64 graphics.
- SSX 3 //PS2. Snowboarding, but trust me, it's pretty awesome.
Besides that, if you're into it, flight sims can be a fun challenge, but really only worth it if you have a joystick and throttle. X-Plane is a good bet for that.
Come to think of it, I have a lot of violent games.