Why are some universal entities round and others are flat?
Preliminary note: there is a continuity of more or less flattened shapes. No macroscopic objects are really spherical, or really flat. Take Jupiter: it has a rotation period around its axis of 10 hours, and you can clearly see that it is an ellipsoid. It's the centrifugal force, combined with the gravitational attraction, that shapes these objects.

Now to your question: Planets and stars are dense bodies, and rotate as single objects. On the other hand, the Oort cloud, Saturns rings, stellar clusters and galaxies are made of independent particles, free-floating in lots of empty space. Depending on the formation history and gravitational environment (e.g., Saturn and its moons) of these entities, the orbits of these individual particles can be more or less co-aligned, and form a more or less spherical clouds.