A world that floats like a leaf

It's a strange thing that fantasy world-builders will happily allow for biology that defies reason, but when it comes to the shape of the world they stay shackled to the globe.  Suppose that there is a world that isn't a sphere.  Suppose that it has a different shape, but that the logic of that shape still gave its creatures a day to day experience that is easily imagined.  Where would imagining such a world take us?