Saturn has a large number of moons. The precise figure is indeterminate, as the orbiting chunks of ice in Saturn's rings are all technically moons, and it is difficult to draw a distinction between a large ring particle and a tiny moon. As of 2007, 60 moons had been identified, plus 3 unconfirmed moons that could be large dust clumps in the rings. Of those, 52 had been given proper names. Many of the moons are very small: 34 are less than 10 km in diameter, and another 13 less than 50 km.[53] Only seven are massive enough to have collapsed into hydrostatic equilibrium under their own gravitation. These are compared with Earth's moon in the table below.

The current thinking is that there are 63 moons orbiting Saturn.

Saturn has a total of 60 moons, many of which were only discovered in the last few years - 52 of them have received official names. Believe it or not, this isn't the most in the Solar System (Jupiter has 63). Most of Saturn's moons are quite tiny, just 2 to 3 km across, and would be considered merely comets if they weren't orbiting around Saturn. Saturn does have some larger moons, including the second largest moon in the Solar System: Titan. Saturn's innermost moon is Pan, circling the planet at only 134,000 km above Saturn's center. The largest inner moon is Mimas, at 397 km across, and orbiting about 185,000 km from the center of Saturn. Then Enceladus at 238,000 km, Tethys at 295,000 km, Dione at 377,000 km, Rhea at 527,000 km, Titan at 1.2 million km, and finally Iapetus at 3.56 million km. More than 35 of Saturn's 60 moons orbit at a distance of more than 10 million km from the center of the planet, and this makes is likely that further moons will be discovered at even more distant orbits. Smaller moons - moonlets really - have been uncovered at gaps inside Saturn's F-Ring, and it's unclear if they'll ever be recognized as moons. For some of the smallest moonlets, Cassini can't image them directly. Instead, the spacecraft was only able to find them because of the propeller ripples they leave as they churn up material in Saturn's rings. This article reports on the discovery of Saturn's 60th moon, and here's a photograph that contains three of Saturn's moons all in the same image. Here's a general article on Saturn's moons, and further information from the Cassini/Huygens mission. 60 moons: http://www.universetoday.com/guide-to-space/saturn/how-many-moons-does-saturn-have/

1) At the moment, 60 have been discovered and confirmed: "1. Mimas 2. Enceladus 3. Tethys 4. Dione 5. Rhea 6. Titan 7. Hyperion 8. Iapetus 9. Erriapus 10. Phoebe 11. Janus 12. Epimetheus 13. Helene 14. Telesto 15. Calypso 16. Kiviuq 17. Atlas 18. Prometheus 19. Pandora 20. Pan 21. Ymir 22. Paaliaq 23. Tarvos 24. Ijiraq 25. Suttungr 26. Mundilfari 27. Albiorix 28. Skathi 29. Siarnaq 30. Thrymr 31. Narvi 32. Methone 33. Pallene 34. Polydeuces 35. Daphnis 36. Aegir 37. Bebhionn 38. Bergelmir 39. Bestla 40. Farbauti 41. Fenrir 42. Fornjot 43. Hati 44. Hyrokkin 45. Kari 46. Loge 47. Skoll 48. Surtur 49. S/2004 S7 50. S/2004 S12 51. S/2004 S13 52. S/2004 S17 53. S/2006 S1 54. S/2006 S3 55. Greip 56. Jarnsaxa 57. Tarqeq 58. S/2007 S2 59. S/2007 S3 60. Anthe " Source and further information: http://solarsystem.nasa.gov/planets/profile.cfm?Object=Saturn&Display=Moons 2) have a look at this wonderful documentary: Carolyn Porco: Fly me to the moons of Saturn "Planetary scientist Carolyn Porco says, "I'm going to take you on a journey." And does she ever. Showing breathtaking images from the Cassini voyage to Saturn, she focuses on Saturn's intriguing largest moon, Titan,with deserts, mudflats and puzzling lakes, and on frozen Enceladus, which seems to shoot jets of ice." http://www.youtube.com/watch?v=xxXa9pxwzoY (the last minutes are a BMW commercial)