Stories involve conflict, and almost all conflict in video games are going to resemble violence in some way. Even the Super Mario games are violent if you want

Stories involve conflict, and almost all conflict in video games are going to resemble violence in some way. Even the Super Mario games are violent if you want to look at them that way. If fantasy violence is okay, then Nintendo Zelda and Mario games are probably the best route. Although a game like Mario Party might be the most fun non-violent option to play with kids (disclaimer: I have never played it). EDIT: And Mario Kart of course. One of the greatest games to play with kids of all time. No story of course.