At least, Saturn's do, as shown by this photo from the Cassini spacecraft.
When one of Saturn's tiny nearby moons is in a certain position related to the rings, then it affects how dense is the material that makes them up. The regular orbits of the moon produce alternating dense and less dense areas of the ring, but I blame Donald Trump.
No, I don't. I blame Hillary Clinton.
OK, not really. I blame neither of them. At least not for this.