The universe teems with flat stuff. Most galaxies, including the Milky Way, are quite flat and (relatively) thin pancakes of stars. All planets of the solar system (real planets, not Pluto) orbit pretty much on the same plane. Unsurprisingly, it’s no coincidence.
Galaxies and star systems form the same way: coagulating clouds of gas—though at obviously different scales.
Imagine throwing a plume of gas or atoms in space. Push them in random directions: some one way, some another, some up, some down. Unless you cheated, they bump into each other and, because of gravity, clump together. When the atoms didn’t collide head-on (ie, most of the times), these clumps spin. Clumps themselves attract each other and collide into bigger spinning blobs.
After each collision, the atoms and chunks of atoms align, canceling out all of their opposing motion, but keep spinning (in fancy physics terms, it’s called angular momentum conservation). You can see the blobs in the video up here as a forming galaxy seen from “above”.
Slowly but surely, the whole cloud flattens to a plane. If it’s a galaxy, it forms stars on that plane, whereas in the Solar System it became that begot the orbital plane.
Other planetary systems and galaxies spin too, but each inclined its own way, because they formed from different clouds of gas.
But if planets and stars also form by congealing gas, why aren’t they flat as well?
The reason is that planets and stars are much denser than galaxies. Being closer to each other, their clumps of gas feel a stronger gravitational pull to the center of the blob, that wins over the mechanism that would keep them flat. So planets and stars become spheres.
Saturn formed across all the stages: most matter coalesced in the huge (clearly spherical) planet, but a little formed some of its many more or less round moons, finally the last faint leftovers ended up as the iconic, extremely flat rings.
If you want more
- A long but excellent post on planets, galaxies, and roundness by the great Neil DeGrasse Tyson
- Minutephysics has a cool video that explains this more technically, and shows why it can only happen in a 3D universe