Anime can be awfully brutal, and that characterization causes people to wonder whether or not non-violent programs even exist. But there are actually plenty of shows that don't involve physical fighting or gore. So if a fan wishes to shy away from people assaulting each other, but still wants to experience an engrossing story, a great anime would be A Place Further Than The Universe or Space Brothers.
Even though it skips out on the ferociousness, non-violent anime isn't always appropriate for children. While many series are perfectly fine for young viewers, others contain mature themes that don't include physical fights. After The Rain is a strong example of this, dealing with a 17-year-old girl's crush on an older man. Others, like Shirobako, focus on the working life of adult characters, which would likely bore a young viewer.
Mushi-shi is a gorgeously animated series about a world dominated by mushi, elemental life forms with magical abilities that range from creating sentient swamps to granting psychic powers to human hosts. In each episode, Ginko solves problems created by these creatures, and learns more about them. Because mushi can occasionally be dangerous to humans, this anime isn't completely without violence. However, its quiet mood and emphasis on harmony with nature nicely offset those brief moments of conflict.
#46 on The Best Supernatural Anime
K-ON! is an example of the slice-of-life genre, and there's nothing violent about it. When amateur guitarist Yui Hirasawa joins the Light Music Club, she has no musical skill. Her fellow club members aren't thrilled, but if they want to keep the club from being disbanded, they'll have to show their new member the ropes. While creating music, the club members form meaningful friendships and learn to express themselves through art.
If you want to go camping, but don't want to deal with the inconvenience or the weather, then watching Laid-Back Camp might be your best option. This is an anime about a group of girls who take to the great outdoors, enjoying each other's company, eating delicious fire-cooked meals, and learning valuable survival skills.
Tripping and falling is a common occurrence in this anime, especially for Nadeshiko, but no one gets seriously hurt, and no one intentionally tries to hurt anyone else. This is a feel-good, educational anime that will leave you contemplating your own future camping trip.
A Place Further Than The Universe
Mari Tamaki doesn't want to let her teen years pass by her without taking advantage of her youth, but anxiety is holding her back. When she meets Shirase Kobuchizawa, a classmate who is determined to go to Antarctica, she feels inspired to join her. Unless you count roiling waves powerful enough to induce seasickness, frigid weather, or other hazardous Antarctic conditions, there's no violence in this anime. It doesn't need it; the nuanced coming-of-age story and unique setting are more than enough to sustain this anime.