I really like games with awkward controls, or controls that take some learning. A lot of old games seem to work like this, but for some reason mastering their control is approached as a part of mastering the game, rather than as a deficiency in their design.
This post is to get the ball rolling, the mind ticking, and to be somewhere to dump ideas.
Ideas:
Probably any genre with RC movement will work.
You are most welcome to make suggestions, or use the idea yourself, like EffBee's ace Pretend You're Platforming. I doubt I'm the first to come up with it!