When Mark Twain came home after visiting 5th Cell, he came up with his most famous sentence: "they did not know it was impossible, so they did it!" 
The Scribblenauts games allow the player to just type the name of items to make them appear: you thus may spawn a "blue platypus", equip it with a "diving mask" and then throw it into a "tiny black hole". The game recognizes tens of thousands of words, which is pretty amazing in itself. A creative player does not even need any level to have fun: I have spent countless hours on the main menu just trying things out.
If I remember correctly, my first true experiment aimed to discover how many crocodiles were necessary to kill God, but I got bored before I found out. God kicks massive ass.
There are roughly two types of levels in Scribblenauts. Firstly, those in which the player must go from A to B. Reaching the exit may get quite boring as the player ends up applying the same solutions, which is a pity; but with the ability to spawn an infinite number of helicopters and giant squids, creativity is not really necessary to overcome any obstacle.
The other type of level can get very creative. These ask the player to write relevant items or creatures into the level. The notion of relevance here depends on a brilliant lexical fields system: each item is tagged with several themes, categories, species, physical properties and so on. That's how, when a level asked me props for a horror movie, I was able for the first time in my life to complete a video game challenge using a dead horse. What a delight!
The Scribblenauts games have their flaws but they are certainly unique, and give the players many occasions to be creative: a huge number of options from many accessible grammars (from everyday life to cultural icons such as the Great Old One, Cthulhu), an immense number of choices, various situations susceptible to trigger inspiration and a never-seen-before pleasure of guessing the myriad of options the developers stuffed the code with.
Finally, I have to mention the game that already gave millions players from the whole world the craziest ideas... Ladies and Gentlemen, let us discuss, review, and praise Minecraft (Mojang).
Minecraft obviously qualifies as creative gameplay. Many players have spent hundreds of hours digging mines, designing automated rail tracks and building rainbow-colored cathedrals in this amazingly compelling construction game. The game world is very hostile, yet very simple to alter. In a few clicks, players may move mountains, build castles, and excavate dungeons.
Minecraft: changing the world has never been so easy.
Minecraft never tells the players what to do. They do not have a story objective, whether short-term or long term. How come Minecraft is not a mere level editor?
Well, the game plays with our most instinctive urges in a very clever way. The omnipresent hostility gives players an objective: survival. They are always no more than minutes away from nightfall and the horrors it spawns. If they want to survive, they need to find a shelter. This urge to find a safe place has been important to mankind ever since wild things realized we were mouthwatering. Architecture has bloomed into an amazing art form, but it all started as just an attempt to get away from dangerous beasts (including other homo sapiens).
So the game has a very strong objective. Players have many ways to stay alive: big strong walls, armors, weapons, traps... hence a large array of creative strategies. Crafting these tools requires raw material so the players have to explore the world. This exploration leads to encounters, discoveries and... ideas. Minecraft has a tremendous potential for opportunity creativity, but its world being very static (apart from systemic or random events such as trees growing or monsters wandering), it allows for long-term creativity just as well.
The gameplay and the game world share a common grammar, mixing unique memorable creatures (especially the creepers), very simplified real-world mechanics (sand is "cooked" to make glass) and classic fictional elements (zombies are tough and slow).
The simplicity and clarity of the game semantics allow players to keep thinking about the game even after they stop playing .
I suspect many other things are at work to make this game a wonderful creativity enhancer: the mindlessness of block-piling , the regions' consistency ensured by the biome system, the absence of a clear goal pushing players to find a meaning to their adventures beyond survival... Minecraft would deserve an entire feature. One thing is for sure: it makes gameplay and creativity a happy couple.
We have discussed how creativity is the way we combine old ideas to create new ones. Inspiration is the process of generating those ideas but creativity goes beyond ideas: it is a problem-solving ability and requires a large number of possible choices.
On the other hand, we have established that gameplay requires that the players take action to overcome obstacles and reach an objective.
We must remember that computers are unable to identify creativity. We can only give the player room for creativity and try to stimulate it, but it cannot be rushed.
Gameplay can leave a lot of room for several aspects of creativity, just not in the games you would expect at first.
There's no arguing level makers and modders are a creative bunch. Kudos to them! But while they build stuff for the community, they temporarily step out of the realm of gameplay.
Customization usually has no impact on gameplay. When it has, conflicts may emerge between the player's creative motivations and the gameplay objective.
As creativity is a tool, not an end, its most efficient application is in complex problem solving, strategy, tactics or open-ended systems. This requires solid, consistent and deep gameplay systems.
Here is an overview of the eight forms of creative gameplay we've identified here :
Why does creativity matter? As a human ability, it is a gift, intrinsically part of our nature. This skill may benefit everyone, and it may be encouraged, trained, challenged... I may be biased on the matter, but I think games are the best medium for that.
I am not only talking about serious games here . But as Raph Koster advocates in A Theory of Fun, games are all about learning. Creative gameplay is good for you.
The current trend of connected media is all about empowering users: social networks allow them to share information about their own lives, level editors give them the ability to tailor their experiences to match their idiosyncrasies, and the increasing success of mobile devices means electronic entertainment is available everywhere at any time.
For players, creativity can make all the difference between mindless button-mashing and unique insightful experiences. Allowing players to get creative may expend your game's lifespan and increase its virality: playing Armadillo Run during lunch breaks taught me how open-ended gameplay makes people stop behind the player to give advice. These people end up buying the game to try their own solution.
By tackling the very subtle matter of creativity, we may also learn how to deal with other subjective issues, such as moral choices. When gameplay uses the same grammar as the game world, then choices made by the player may have deep, emergent, and meaningful consequences.
For my first article on Gamasutra, I would like to thank… well, Gamasutra, obviously, not only for releasing it but also for their very motivating support. A thousand thanks to my wife, but only hundreds to each person who helped me gather information and gave me advice and data: Thomas Bidaux, Samantha Whale, Thierry Perreau, Nicolas Debeljak, Damien Chevalier, Adrien Pelov, Camille Lescaudron, Régis Bonnessée, Philippe Baille, Christian Cirri, Sylvain Gadonna, Antoine Guyard, Marc Rutschle, and all my geeky colleagues for the past eight years.
I would also like to cheer with a grateful wink all the people who don't know me at all but showed me the way through their work: Jesse Schell, Daniel Floyd and James Portnow, Jean-Louis Roubira, Bill Waterson, and many more I ungratefully forgot. I'd also like to thank the following creative companies: Mojang, 5th Cell, Maxis, Lionhead and so many more.
You may give me feedback by commenting or reaching me via LinkedIn (provided you are an interesting person). I hope you enjoyed reading this. Keep up the good creative work!
 Disclaimer just to be safe: this story is not true. Mark Twain died in 1910 and never played Super Mario, which proves he wasn't really into video games.
 I have once been in a boring work meeting where three people (including me) were drawing the plans for their next Minecraft buildings while some producer guy was waffling on and on.
 I believe piling things is as useful as dishwashing when it comes to triggering brilliant epiphanies.
 Minecraft could have been cited as a perfect example for at least half of these manifestations of creative gameplay.
 A serious game teaching how to improve creativity may be very efficient though.