This post is an index of "Challenges" from the before-times: the Minecraft Forums. This is an incomplete list. These challenges are made to be used on any world, and were not made by me. The main criteria I've been looking for when indexing these is ones that have room for creativity; not just "get [x] items" or "don't use [y]", but "build [z]" being the focus.

These are mostly indexed from my memory than from any other list, so many are probably missing.

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Challenges with Working Links

• Cubeaism. Cubeaism is a roleplaying concept mixed with challenges. Essentially it's a list of deities that represent gods in the Minecraft universe, with specific requirements for each: permitted and banned tools, weapons, armor, food, and shrines. Each god typically requires you to do certain tasks or build certain things.
  
  
• Refugee to Regent. This is a long, complicated one based on the City Building challenge. It supports modding, and has two versions: a completed "Classic" version (linked at the bottom of the main page) and a work-in-progress new version. This one attempts to simulate the development of cities over stages.
  
  
• Tree Spirit Challenge. The Tree Spirit challenge is the simplest one: the first tree you cut down becomes your base tree, and you are unable to destroy its bottom block. You must always be connected to the stump by a path of logs. This one is from before the End update; I'm not entirely sure if you can manage to kill the ender dragon with it.
  
  
• Castle Building Challenge. The Castle Building Challenge is another classic one; you must build a castle in stages based on the Minecraft materials, retrieving certain items to keep in storage and vaults. The castle has requirements on what all you build into it, such as needing a wizard's tower.
  
  
• City Construction Challenge. This one is no longer accessible from the Minecraft Forums; this is a link to the Wayback Machine edition.
  
  
• Fantasy City Build Challenge. This one is derived from the City Construction Challenge. It's the same idea, but with more of a fantasy theme to it.
  
  
• Nuclear Apocalypse. One of the classics; a more complicated version of the "can't go on the surface" challenge many people have tried from the start.
  
  
• The Water Spirit Challenge. Like the Tree Spirit, but probably easier, considering you can travel across all the water instead. I can imagine this one working very well with the new Aquatic Update features and themes.

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Details on those Without Working Links

• "Underground Challenge": the bog standard "only stay underground" ones. Never go on the surface after cutting your first tree.
  
  
• "Zoo Challenge": collect at least 2 of every mob with name tags, including hostile mobs, and lock them in pens with "natural" exhibits.
  
  
• "Treetops Challenge": you must only build on treetops, connecting them by bridges between them. You can mine and collect resources on the ground, but all buildings must be on top of trees.
  
  
• "One Chunk Man": you must only use one chunk for all your building. You can leave the chunk to get resources, but everything you buidl has to be inside the single chunk.
  

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If you know of any others that I missed, please link them in the comments.