It is also theorized that the reason that the reason why Saturn's rings do not do this(though this could just a matter of time that we are now viewing them at) is because they are prodomonantly ice crystals which constantly bounce into each other breaking and re-freezing. IE why we can see them at all(reflective surfaces on the ice) rather then them be covered with dirt & dust and rendering them unreflective.

Further more to your question I "think" any planet or even any object could have rings, its just there are many factors that go into play and singularly it is REALLY hard to see them, and we only have our galaxy where we would be able to tell if an object did or didn't have them.