Super Many-o Brothers: Hello Worlds!
Hello Worlds! is a splendid 2-4 player platform game for one player.
Created by clever sorts on the University of Washington Computer Science course, it's at first glance another clutch of 'collect all the shiny things and get to the exit' jumping puzzles. Thing is that you're trying to do this in four levels at once. Move your blobbly pixel-octopus thing in one screen, and its actions will be precisely mirrored in the three others - and affected by them. So, walking across a platform in one will have him apparently floating in mid-air in another, or your progress in one will be invisibly impeded by a wall in another.
It's along the same lines of the mirror/clone system that indie games such as P.B. Winterbottom have dabbled in so frequently of late, but in this one your control is never anything less than direct and absolute. What I find most interesting is how my brain adapts to it - initial panic at the strangeness of controlling four synchronised characters in four asynchronous worlds, soon replaced by keeness of observation, somehow able to monitor all four screens without discombobulation.
Try it. You'll like it. And so will your three imaginary friends.