This may overlap with other questions, but I'm asking what is unique about Saturn in location, properties, etc that is has far more pronounced rings? It's between Jupiter and Uranus and Neptune in size and position. So what's special? Is there some Goldilocks zone of rings formation? Or is it just an accident of history?
Saturn's rings are unique in that a lot of the rings compositions contain new and recycled material. Much of the uniqueness is complementary from Saturn's moons, which play a critical role in shaping and recycling the rings materials.
A great example is the moon Enceladus, which contributes largely to the E Ring. Icy material is ejected from Enceladus, a process called cryovolcanism (spewing plumes of icy materials instead of silicate rock); due to the lack of atmospheric pressure and low surface gravity, Enceladus doesn't hold the material that it ejects, but rather feeds material into the E Ring. Discovered by Cassini, the material is comprised of simple hydrocarbons such as methane, propane, acetylene and formaldehyde.
A contributing factor for the unique shaping of the rings and much of their orbital stability stems from the moons also. Another well known example is the Cassini Division and a process called orbital resonance. Essentially the moon Mimas orbits once for every two orbits for material inside the Cassini Division. As a result of that orbital resonance the material receives accumulation of radial momentum, the effect of such accumulation forces a tug of war with the particles. Mimas attracts the material pulling it into the A Ring as the material increases in velocity, resulting in the division.
Other moons have also been documented to have this effect, such as the moons Pan and Daphnis in the A Ring, however it is thought that the effect from these smaller moons only create a division around 10km in width. Stability can be exaggerated from the F Ring, with the moons Pandora and Prometheus. These moons twist the material into a spiraling vortex, like a horizontal tornado encircling the planet. Processes of stability arise from moon ringlets, such as the Titan Ringlet. Titan has orbital resonance with material in the C Ring and provides radial momentum with the Colombo Gap, the gap is slightly elliptical rather than circular (just as Titan is) and the material is attracted towards Titan in the same pattern, in a process called apsidal precession. This creates a compression and expansion of the rings giving them stability while accumulating velocity due to orbital resonance.
Distortions from the moons on an independent inclination to the rings as they come close to the rings, also pull material from the rings and spread it around in chaos, additionally recycling material.
Each ringlet has an individual story as to the forces which make that ringlet unique, comprising of the orbital parameters of the moons and the unique positioning of the forces around them. Along with material that is recycled in a unique fashion not evident with other planetary rings system.
The uniqueness stems from these factors.