Non-violent games, Google them to download, as I have not the time to post links as of now:
Tetris Gold
S64 Mini golf
Aquadelic
TORCS (The Open Racing Car Simulation)
Acid Bomb (Some might consider this violent, but essentially, its a puzzle game.)
AtmoSphere (type Digipen in the search also)
Toblo (again, Digipen)
Cow Abductor (you might consider it violent, but give it a try)
Ball Racer
Motocross: The Force
Blobby Volley (Kinda odd, but I like it)
TrackMania Nations (Warning: Big download!)
Pakoon (All three are good)
GeneRally
Counterclockwise
RCbasic
Swarm Racer
Note: Digipen requires you to give, I think, your name and age to download their games, but I think you can put in incorrect information and it will accept it.
NoteNote: I have listed no RPGs, as they almost inevitably contain some violence.
If you can't find one, or want to know something about them, ask me. Obviously, listing only non-violent games narrows the list quite a bit. If you want some more violent games, I could start a new thread if you want. I know quite a few good freeware games.