Answer:
Saturn has 62 moons with confirmed orbits, as of March 2011. 53 have been named and 9 are provisional. These are as follows:
Aegaeon
Aegir
Albiorix
Anthe
Atlas
Bebhionn
Bergelmir
Bestla
Calypso
Daphnis
Dione
Enceladus
Epimetheus
Erriapus
Farbauti
Fenrir
Fornjot
Greip
Hati
Helene
Hyperion
Hyrokkin
Iapetus
Ijiraq
Jarnsaxa
Janus
Kari
Kiviuq
Loge
Methone
Mimas
Mundilfari
Narvi
Paaliaq
Pallene
Pan
Pandora
Phoebe
Polydeuces
Prometheus
Rhea
Suttungr
Skathi
Siarnaq
Skoll
Surtur
Tarqeq
Tarvos
Telesto
Tethys
Thrymr
Titan
Ymir
Provisional:
S/2004 S 7
S/2004 S 12
S/2004 S 13
S/2004 S 17
S/2006 S 1
S/2006 S 3
S/2007 S 2
S/2007 S 3
S/2009/S 1
There are countless pieces (of varying materials, sizes, densities, masses, and life expectancies) orbiting Saturn. What is lacking, is consensus on a clear, definition of the term, moon.