I just remembered 2 Icepick lodge games:

Cargo! the quest for gravity

The Void

They're both completely nuts in different ways.

I didn't understand. By "without violence" do you mean without combat, i.e. killing enemies? Or just no gore?

The other way around. I don't mind gore per se, I was just wondering if there are alternatives to constantly fighting and killing enemies as the main objectives. So it's more about gameplay mechanics and goals for me than about PG rating.

I guess suggestions like Bully had me confused. I suppose my next question would have to be what exactly do you consider an open-world game? Since in your OP you included games that I would personally call linear, or just a collection of small levels. In the meantime, I might be able to make a few suggestions:

- Driver San Francisco: You do occasionally have to ram another car out of the road, but most of it is just racing, plus seatbelts are made of titanium and pedestrians all have a magnet up their ass that pushes them away whenever your car dets close, so no one gets hurt in the game.

- Sly Cooper series, in particular 2 and 3. Not a single large map, but each location is fairly big and you are free to explore. Once again, there is combat, but the main gameplay element is stealth so, apart from certain missions and against bosses, you are encouraged to avoid enemies.

- Miasmata. Open-world survival adventure game. You arrive at an island with a fever, you can go just about anywhere, and you must to find herbs with which to treat yourself. The map is drawn by your own character by triangulating your position using points of interest. Never finished it, but I do remember the wildlife can stalk you at night, but I don't think there was any combat.

Not sure if it's relevant to your interests, but I started playing Kholat recently, and I'd say it qualifies as a small-scale open-world game. There's no fighting, few encounters with enemy entities, and the main focus of the game is on atmosphere and exploration. It's a bit similar to Vanishing of Ethan Carter, just with a very different setting and story. If the setting of the game appeals to you, go check it out. I've been playing for a few hours so far and I like it.

https://www.gog.com/game/kholat

Yeah, that's because I was clutching at straws. ;) I'm not really sure where to draw the line, but initially I was thinking about games with a larger area (or a couple of large areas that are connected) to explore and do several activities in, in any order and at your own pace, ideally with collectibles and unlockables and other mechanics that give you a sense of progression and achievement to keep you motivated in exploring the world. Think GTA, Saints Row, Far Cry etc. without the weapons and killings.

I didn't think of Driver; I've only ever seen one of them (maybe 1 or 2?) played on the PS; is San Francisco open world, in that you can drive around freely and accept any missions you want, in any order? Does it have collectibles or other things you can work on outside missions? Miasmata seems to fit the requirements, unfortunately I gave up on it after ten minutes or so because it felt badly optimised and kept on lagging and stuttering despite my GTX660 ...

I guess this might not be the kind of (light-hearted) open world game I had in mind initially (no side activities I assume?), but it seems to fit in well with suggestions like Miasmata. There have to be quite a few games in this specific genre nowadays, I think. Maybe Firewatch, as well? Or Eidolon (although it features bow and arrow and hunting, I think, which might put off some players more than killing humans ;) ).

I can't enjoy Minetest even with mods and some don't even install properly for me.
It lacks essential blocks, features, isn't fleshed out ... and it hasn't got that awesome music.
You are probably the best person to ask. :)
Is there any fleshed out creative mode or cheat mode for Terraria that is maybe added by a mod? Is there any way to temporarily turn off the aggressiveness of the enemies and maybe give yourself resources to build structures?

You shouldn't need one until Hardmode. Ask in the Terraria forum though. Someone in there will know for sure.

Are you only asking for games for PC, or including consoles?

Okay, thanks. :)
It's not about "needing" one, though, but about giving me more ways to play the game.

mmm, some Need For Speed episodes had the "free-roaming" aspect and the latest version of Test Drive too I think. Midnight Club on PSP is open-world (reminds me I should replay it).

Or you can do like me and play GTA Online "pacifically" by just doing races and on-the-side stuff (maybe that's why I still haven't reached level 100 after 250 hours of gameplay ^o^). Maybe even wasting hours just to make some in-game pictures :o)

GTA series (up to San Andreas). There is no violence, its just a computer game!

Yes, SF has free roam, you can choose the order of your missions, you can complete driving challenges scattered around the world to get more currency used to buy cars and upgrades, and collect movie tokens to unlock special missions inspired by famous chases from classic movies.

I'm sorry to hear about Miasmata. I played it years ago on a GTX570 and didn't see any problems, but these things can be unpredictable sometimes.

The only console I own myself is an old PS2, but since I'm asking more out of curiosity, trying to learn what games there are in general, I guess console suggestions are fine!
Sounds interesting, I'll keep an eye out for it. Have you played it on PC, and if so, on what OS? I've read some reviews saying that the controls are too sensitive on PC when playing with mouse and keyboard or that it doesn't work well with Win 10. I have Win 8.1 myself and I own an Xbox controller, but I've seen some console ports with bad driving controls on PC (Saints Row 2, Burnout: Paradise - another non-violent open world game, btw), and that can really ruin the experience if the games are all about driving ...