If ice and rock form rings around a planet like Saturn, why don't rings form around Earth from all of the broken satellites and other material around Earth, or will they eventually? I would expect at least some form of coalescing by now.
It might. From Wikipedia:
"The Kessler syndrome (also called the Kessler effect, collisional cascading or ablation cascade), proposed by the NASA scientist Donald J. Kessler in 1978, is a scenario in which the density of objects in low Earth orbit (LEO) is high enough that collisions between objects could cause a cascade—each collision generating space debris that increases the likelihood of further collisions. One implication is that the distribution of debris in orbit could render space exploration, and even the use of satellites, unfeasible for many generations."
..."The 2013 film Gravity features a Kessler syndrome catastrophe as the event that sets the plot in motion"