I played What We Possess for the first time a couple weeks ago. It's a no-prep GM-less story game/RPG where the players play ghosts haunting a location, collectively pushing the living towards helping you accomplish a goal or solve a mystery. Just about everything--the location, the living people and animals plus the things present, the minimal details about your ghost, the goal or mystery, and the clues uncovered--are all randomly pulled from card decks.
It requires a lot of improvisation and trust that a story will emerge. The game provides set pieces and expects you to work out what the story is, collectively. It says: Here's a bunch of stuff to play with, now start moving things around, fill in the details and go work out how your ghosts accomplish their goal. Or maybe they won't, running out of energy and fading into the void before they can move on, that's an option too.
(I've tried several times to write how the game is played, but it's gone over a toot's character limit each time.)
It was everyone's first time playing it and it definitely felt shaky for the first couple of scenes. Once we picked up some momentum, a story did start forming, we arranged the various pieces into a plot and were able to wrap it up in a couple of hours. Fun, but we had to sit with a lot of uncertainty during play.
The photo is my attempt to recreate our setup at the end of the game, since I didn't think to take a photo at the time.
Be a Horde of animals
Pretending to be human 
Kind of badly
That's the game. 
Good luck!
