I had a hard time choosing one of my dream games, as you can only submit one idea. I decided to go with the one that is feasible by today's game development standard.
This dream game is a grand Civilization like, tun-based strategy but without the earth's history in the background.
I see it taking place far in the future, where humanity was almost wiped-out. Instead of civilizations (like Inca or Spanish) you would choose your tribe from a set of backgrounds (humans who survived all those years in vaults, tribal humans, new-humans or even an AI) and add a set of traits (like defenders, gatherers etc.) You would start with certain technologies, but You would not have to progress trough tech-trees in a lineral fashion - instead, you people can adapt many approaches (technology-like or magic-based) to achieving the same goal. The tech-tree would change while you play, so You can mix and match your approach, making your people fantasy, realistic or something in between (like steampunk for example).
A lot of game mechanics would be handled by "traits": tactics for units, beliefs of your people, even their physical traits. So each unit and building would have it's own set of traits represented by a small icon. This is to encourage a moding couminity to come up with new traits and technologies to expand the game even more. With traits like that, you can easily develop rock/paper/scissors approach to different aspects to the game.
Other civilizations would react to you based on how similar they are to yours (in "race", traits, technology etc).
You could create your own buildings and units from "ready parts" of technologies you discovered, making every civilization unique in a way.
On top of that, a lot of the game would be procedurally generated, from maps you play on, trough random events and even some random resources (are those animals safe to keep, maybe they make a great mounts?).
It would be a true-sandbox grand strategy, that focuses on player's immersion.
I could write a lot more about it, but I feel like this post is long enough.
Maybe, one day, when the stars are right, I will be able to bring this game idea to life.