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The Scribblenaut series?
You may want to check out Space Engineers, it's all about create things, more or less like Minecraft in space. It's in early Alpha stage and the developers are known for promising more than they can deliver from previous games so keep that in mind.
Line Rider.. There are some amazing YouTube videos.
Have you played Universe Sandbox? It may be more about discovery than problem-solving and I haven't tried it yet but it definitely appears to spur the creative mind. You can download a free version on the official website:
http://universesandbox.com/
Tomorrow I might compile the suggestions into a list in the OP, as I had done with a former "contemplative gaming" thread. But in the meantime, I note that we forgot about Kerbal and we are unforgivable.
Post edited July 09, 2014 by Telika
all those game mods come to mind, like the one that became Dear Esther

How about Minecraft? Spore? RPG-Maker?
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Melhelix: If you can manage the difficulty, Dwarf Fortress reigns supreme.
Oh yeah. "Go creative and try to build whatever you imagine" is the main interest in this game. Some players even designed an in-game calculator, using pumps, water, magma and pressure plates. (I saw the blueprint, and THAT is what I call a monster, overcomplex project. My own are mostly in the "grand architecture and sadistic traps" categories)

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Telika: But in the meantime, I note that we forgot about Kerbal and we are unforgivable.
Yes, we DID forget it, didn't we? (covers his head in shame)
Age of Empires 2.

Many civs to choose, many strategies on one map, many quick decisions like walling in the enemy's resources with palisades, going with a fwd base...............endless

Pokemon

Many movesets for every 600+ pokes, different ev spreads and many overall playstyles. And a PC online battle simulator!
Many different things to choose from is not what I would call creative, necessarily. While being a great game in itself, the only "creative" part of Age of Empires 2 would be making new scenarios - but this is not really ingame creativity.

To a certain extent, I would say, Open-World-Games like the Elder Scrolls series could be considered creative because of how they allow the player to play their very own story and do whatever they want if they choose so. Of course, the modding possibilities are a whole other thing altogether, though again, this is not exactly happening ingame. Other than that, I liked the building part of the Sims always a lot more than the actual playing. One could say that building a castle in Stronghold is kind of creative, but you are relatively restricted by the purpose of it. Rollercoaster Tycoon, however, can be a very creative experience. You are not required to use themeing parts in a way that they actually make sense or look good, but it is just way more fun if you think a little about what your park should look like and try to build it as beautiful as possible. In the second game you certainly have enough parts and possibilities to build basically anything you want, but it can become very fiddly at times. Still, I cannot recommend this game enough.

However, most games are only creative within the boundaries of their own rules and provided possibilities. Finding ways to overcome these either within the original game or from outside with mods is where the real fun begins, in my opinion.
Cogs
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Pherim: Many different things to choose from is not what I would call creative, necessarily. While being a great game in itself, the only "creative" part of Age of Empires 2 would be making new scenarios - but this is not really ingame creativity.

To a certain extent, I would say, Open-World-Games like the Elder Scrolls series could be considered creative because of how they allow the player to play their very own story and do whatever they want if they choose so. Of course, the modding possibilities are a whole other thing altogether, though again, this is not exactly happening ingame. Other than that, I liked the building part of the Sims always a lot more than the actual playing. One could say that building a castle in Stronghold is kind of creative, but you are relatively restricted by the purpose of it. Rollercoaster Tycoon, however, can be a very creative experience. You are not required to use themeing parts in a way that they actually make sense or look good, but it is just way more fun if you think a little about what your park should look like and try to build it as beautiful as possible. In the second game you certainly have enough parts and possibilities to build basically anything you want, but it can become very fiddly at times. Still, I cannot recommend this game enough.

However, most games are only creative within the boundaries of their own rules and provided possibilities. Finding ways to overcome these either within the original game or from outside with mods is where the real fun begins, in my opinion.
I have to disagree with you about AoE2 (and this is one of the very few sites where discussions take place, and not flame wars, as you probably know, so I'm not trolling). Creatingg different build orders. Like how many vills on which resource to get X number of X units in X minutes, and doing stuff like making a small box around your mangonnel so its minimum range is removed etc does require a lor of creativity.

Of course, modding is an entirely different type of creativity. Most people don't have the skill for it but those who do can, as you said be free from the limitations of the games rules. While modding allows a higher degree of creativity, I still believe RTS games allow the most creativity within the rules of the game.

RTS=lego bricks. You can do a lot, but following certain rules.
Modding= plain canvas. You are not limited in any way to express your creative freedom.
I agree with Aniki about Line Rider. I am not a big fan of physics+sandbox games (e.g. World of Goo), but I am a fan of Line Rider.

Minecraft should get more mentions. People have used that game to build everything from reproductions of entire cities to scientific graphing calculators to a cat-spewing volcano (search "catsplosion" for a how-to).

I would also say that some RPGs, like Fallout are pretty flexible about in-game life-choices. (The developer thinks of EVERYTHING.)

You might not think of Scorched Earth as a very creative game, but creating a bunch of short one-liners when you attack/die that fit on the screen involved a lot of thought. Ditto with the extensive Civilization and DOOM mods that came out.

Another personal favorite of mine would be Magic Pengel: The Quest for Color for the PS2. It's a monster-breeding type game where you fight over crayons. Yup. With each colored crayon, you can draw a shape. Stats depend on the shape. You start with a red crayon, so your first creature is likely going to be a red cylinder, maybe a giant foam hand, that bounces around. With more crayons, you can draw green wings or brown horns or purple legs... and watch that mess animate.
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Shadowstalker16: I have to disagree with you about AoE2 (and this is one of the very few sites where discussions take place, and not flame wars, as you probably know, so I'm not trolling). Creatingg different build orders. Like how many vills on which resource to get X number of X units in X minutes, and doing stuff like making a small box around your mangonnel so its minimum range is removed etc does require a lor of creativity.
I agree that they certainly require creative thinking and RTS games including AOE 2 have always been one of my favorite genres, but I don't think they are creative in the way the OP is looking for. Yes, you have to figure out the most efficient way to build your village and organize your villagers, but in the end, the ultimate goal is the same in most missions and you don't have any real choices or freedom which I would call "really" creative. Interpreted the OP more in the way that the games include creative elements mainly for creativity's sake, give you freedom to do what you want - to a certain extent. In AOE and other RTS games, you are usually limited in your creativity by the mission parameters and you build your base based on ho efficiently it can be defended (yes, this is a creative effort, but again, not enough for me to have it pass as a creative game). And then I would say that games like Caesar III and it's accompanying city builder games are more creative than plain RTS games (this is not meant to be derogatory, as I said, I love RTS games), since you can actually try to build a city that is not only efficient but also looks good and still have success in achieving the goal.

But maybe I am just too picky about the term "creative" ;-)
I agree ;)

BUT,
I was talking about multiplayer where the goal is to defeat your enemy. You are given very little limits as is related to creative freedom. What is functional can be a point of view. In competetive AoE2, in random map, if you build a more asthetically pleasing base than one that is functional (ie, a wall of buildings :D), you get raided.

But as you said; it still does not mean full creative freedom (far from it). I can't still choose how my vills chop wood or just do WHATEVER I want. Indeed, I saw creativity differently.

Creativity has a different meaning who ever you ask. To players of more limited RTSs like SC (no offense), they may say creativity is based on micro and base-building. If you ask people who play tactical shooters, they'll say creativity is finding new ideal locations on the map. Anyway, creativity is still manifested most in putting stuff on a paper , on a plate or in a CD. Ie, creating something from nothing. So as to creative games, I agree that city building games have the most creative freedom since you aren't bound at all.
Rollercoaster Tycoon 1-3? Anyone?