The Path. It's a bit of a adventure horror walking simulator set in a small open world. There is no explicit violence although it is hinted at times. I guess I should qualify that while it IS open world, it isn't open ended, meaning each character's level has an ending, you just have to hit all the triggers or just head straight for the bad ending(s).

Minetest is a Minecraft clone that is open source (and available for Linux), it has no monster mobs installed by default.

Planet Explorers is a voxel-y Outcast-ish open world "go explore and build stuff" game that has a violence-free build/adventure mode, however the main campaign does have fighting.

Lego Island was the best thing in the world when I was a kid.

Funnily enough I generally don't have a problem with violence in games, even when it's not particularly justifiable (like going on a rampage in GTA), though I'm not sure if playing newer games with more realistic graphics would change that. But what I did have a problem with was hunting in Assassins Creed 3. Slaughtering redcoats was fine, but killing defenceless deer really put me off.. I only ever hunted to complete missions and never enjoyed it...

As for non violent open world games... I'm struggling to come up with anything that hasn't already been mentioned. Most open world games I can think of contain elements of violence.

Does Garry's Mod count as open world. From what i remember you couldn't shoot anything because there was nothing to shoot at. It actually felt like a glorified level editor for Half Life... what some people see in some games...

Gonna propose you Euro Truck Simulator 2. It's something about it that makes me play it over and over again, it's relaxing, simple, i don't know, it's just awesome. And i'm not a big fan of racing/driving games in particular.
As you are from Germany, your country it's pretty well represented in the game. You'll have a blast driving your truck and recognizing landmarks from your country. Modding community it's pretty crazy too, you will find a lot of content as mods.

I think the Bethesda games are just too long, if you actually want to do all the sidequests. After some time the open world gameplay always gets a bit old and repetitive. I prefer these games to be in the 20-40 hour range like the Saints Row or Far Cry games. The only open world game that hooked me for over 100 hours was the Nehrim standalone mod for Oblivion. That world actually felt interesting enough to fully explore, but I never got very far in the official Oblivion or Skyrim campaigns or Fallout 3 or Kingdoms of Amalur, because their worlds are so big that they intimidate me, and the content they're filled with doesn't grip me enough for me to stick to them for over 40 hours.

Almost forgot ... Minesweeper!

I haven't played them but what about Disney Infinity and Goat Simulator? The latter is chaotic, but I don't think you could call it violent as such.

What I don't like about Don't Starve or other rogue-like-likes, compared to the average open world game, is the complete loss of any progress you've made when you die. The attraction of open world games to me is precisely that you're constantly making progress on the map, collectibles, unlocks etc. that is stored for good, so that you can't lose it anymore.

You call stepping on a mine and getting blown up "without violence"? :P

Where are you from, Beirut? :P

Oh right, I forgot about that. Of course, it's all about destruction, but not necessarily about killing, so I think it's fair. Sadly, I think what I've said about Don't Starve applies to Goat Simulator in a similar way. AFAIK your game is not saved when you quit, so all the "progress" you make in the game is illusionary and not very satisfying.

Yeah, I don't think that Goat Simulator is too focused on things like progress. Or at least that's the impression I get.

I think I actually have a greater problems with it if the violence is presented as justifiable, compared to just blowing shit up for fun. I mean, there is a difference if a game just allows you to be violent, or if it orders you to be so and rewards you for it (unironically), and there's another difference between the game just being totally bonkers, with unmotivated violence, or the game trying to manipulate you into a "righteous" fury, presenting you good reasons (or excuses) to enjoy all the violence against the "bad guys". And I think the closer it is to reality or RL reasoning, the more I'm put off by it.

X series might qualify. Combat is almost entirely optional (although, truth be told, you'll actually have to fight constantly with the terrible interface). It's more of a first person tycoon than a space sim...