Also, LittleBigPlanet...
Nope, that's violent. Get the MGS pack and the paint gun and you got yourself a weapon. Even without it, you jump on the heads of enemies to kill them.

Solid Sackboy was pretty cool, stil.

Do minesweeper count as violent?

Nobody dies, so... wait, unless you count that smiley face as the guy you're trying to save.

Actually, I've done just that. I've created digital... analogs (heh) of friends, family, people I hate, Glenn Beck, Howard Stern, and many others and put them in rooms and killed them. They just keep having to go, and I don't let them. I feel evil.

Voilent. You are assimilating (i.e., killing) other cells, some of which are sentient.

Yes.

You kill enemies in both Crash, Spyro and Mario. At least in all games in those series that I have seen.

Then there is no non-violent game at all. Maybe a Teletubbies game or something. :/

Chains & Graveyard.

There are several games without avatars at all, I believe few card games could be considered violent, tetris has already been mentioned, as has peggle, bejeweled and some other games. Minesweeper probably sits in that category as well, even if the spoof movie depicts it differently. Guitar hero and rock band do have some form of avatars or personas in them, but no violence as far as I know.
All those are examples of games that are pretty popular, albeit not often thought of by us more "hard-core" gamers. (quotes, because I'm not sure that's the right word, but couldn't think of a better one)

The Path is out, it is most definitely violent on both a physical and psychological level depending on the girl.
There are. And not just edutainment games made for children.
Off the top of my head:
Girl's Mode -- a Japanese fashion game where the player manages a clothing store and takes part in fashion shows -- no violence in there.
GiFTPiA -- An alternative RPG, the nearest you come to any sort of voilence is a game of rock paper scissors with a monkey (IIRC -- but it's been a good 6 years since I played it).
And the Boku no natusuyasumi series doesn't feature any violence.

If I ever came into possession of a Teletubbies game, I guarantee that violence would ensue almost immediately ;-)

If, as mentioned above, getting a car hit with no visual damage is considered violent, then bending a card, destroying innocent falling blocks, switching and exploding gems, shooting deadly balls that also destroy walls and change their colour can be also considered as violence. Even songs in Guitar hero can be ear-rape then. I mean, come on.
What kind of rules are those, Weclock? Are we talking about kids getting into gaming or adults with no gaming influences?