Kinda depends on your definition of violence.
Physical violence, I'm sure there are some (Japanese dating sims spring to mind, along with Sim games)
But without conflict of some sort there would be nothing to advance anything. Any good story, and this extends to any form of media as well, has an internal conflict being resolved by the actions of the characters, otherwise there literally isn't a story, it would just be people sleeping, eating and possibly watching some television.
Even then there might be some conflict, based again on how broad your search is. Conflict could be as little as 'there's no milk, so I have to buy milk.' This is the conflict of not possessing the artifact needed, and having to travel to the place from whence it can be taken, obtaining thus the legendary vial, paying the toll for its acquisition, and transporting it safely home where it can find new use.
[sub]I want an epic game about buying milk[/sub]