Running off Keira's post, I’d like to see games that don’t just give the player a small set of actions to use exclusively throughout the entire game. Instead, if the programming is simple enough, fill the game with interactions that will be intuitive but are specific to one or a few parts of the game.
If the arms and hands are very basically represented in a game, then simply directing those hands in intuitive motions could accomplish any number of tasks.
If the player sees a ladder, it would be intuitive to simply place a hand on one rung, then the other hand on the next rung, and back and forth as the character moves up or down. Any object could be grabbed by moving the hand over an object and closing the hand.
Even the relatively rudimentary motion-sensing technology of current consoles could be used to make open-ended, explorative gameplay in this way.