When I was a kid I imagined about a racing game where you can choose from a wide range of vehicles and create 'unbalanced' races. For example, a TC racing car vs a Truck, a Formula 1 vs a plane and so on.
Another idea, but not so much about mechanic is for a game concept I call 'Eternal'. Inspired in the premise of Remedy's 'Quantum Break' (but the game doesn't develop in the same universe nor it's a fanfiction). Thing goes more or less like this: Humanity invents time-travelling using something similar to the 'Chrono particle'. So many humans are sent to change historical events (like helping civilizations that where destroyed, kill dictators, etc.) But eventually times start to glitch and break due all the changes. In the end, only 3 persons (2 scientists and the player) remain 'safe' inside a special bunker but they need to fix everything. The scientists idea is to travel back in time to prevent the original time travel. The MC think about not doing that (because it will cause a heavy time loop) but to travel back to every single change made and turn it back. The game would be mostly about going to different places and time periods, figure out not just what was changed but also how things where/should be originally and prevent/fix those changes. (This won't cause a time loop as well? well, yeah probably. This is a vague idea, didn't though it too much.)