Why does Saturn's dust form a flat ring and not a sphere around it?

[kaleidoscope]

Why does Saturn's dust form a flat ring and not a sphere around it?

[mgb_phys]

Initial angular momentum of whatever the stuff came from (the material that formed the planet or an broken moon)
Bulges on the rotating planet create a gravity gradient
Shepard moons tend to compress the particles into a single orbit.

[qraal]

Saturn's rings contain some dust, no doubt, but most of the material is in chunks several metres in size.

The previous reply answers the initial question, mostly. No one is too sure what the rings began as - a moon or unconsolidated material from Saturn's formation - but for a particle to rise above the initial plane of formation of the ringss, it would need a significant input of energy. This is rather unlikely, as that much energy would have vaporised the original ices, so solid particles mostly stayed in the initial orbital plane, and flattened out through the non-spherical gravitational field, plus re-colliding with the ring itself.