The first impulse everyone has to this sort of question is that the rings are little specs attracted to the tiny FE Saturn planet, rotating around it like a miniature version of the big planet operating under a different flavor of "gravity".
But is that really necessary? In practice things like Saturn's rings and the entirety of galaxies actually look completely solid and interconnected no matter the power of your telescope.
Could Saturn be solid?
Could the galaxies be solid?
We already know that the REer's need "Dark Matter" to explain why the galaxies rotate as if they were solid disks. Describing the movements of galaxies has been a challenge to astronomers. According to Newtonian mechanics the bodies towards the interior of the disk should move at a faster rate around the center than the bodies on the outside of the disk. This is exactly opposite of what is observed.
See this quote from softpedia.com:
"According to theory, a galaxy should rotate faster at the center than at the edges. This is similar to how an ice-skater rotates: when she extends her arms she moves more slowly, when she either extends her arms above her head or keeps them close to the body she starts to rotate more rapidly. Taking into consideration how gravitation connects the stars in the galaxy the predicted result is that average orbital speed of a star at a specified distance away from the center would decrease inversely with the square root of the radius of the orbit (the dashed line, A, in figure below). However observations show that the galaxy rotates as if it is a solid disk as if stars are much more strongly connected to each other (the solid line, B, in the figure below)."
Perhaps the simplest explanation is that they simply ARE solid disks!