Twenty three.  When Galileo first saw Saturn‘s rings, his telescope was primitive enough that he could only see that there was something odd about Saturn’s shape.  As time passed, and more astronomers used better telescopes to observe Saturn, a clearer and clear picture emerged.  First it became clear that the mystery shape was a gigantic ring around the planet.  Then a gap was noticed – the Cassini Division – increasing the count to two rings, followed by more gaps, and colour variations indicating more and more rings.  But the number really started climbing when robotic spacecraft began photographing the rings from close distances.  We now know that there are twenty-three rings, and we do not expect to find even more.  The rings are composed of loose particles of rock, shepherded into place by many of Saturn’s tiny moons, so looking any closer will reveal only rocks and not divisions between rings.