iPhone system font
To the delight of font purists everywhere, the iPhone system interface uses Helvetica or a variant thereof.
The original iPhone, iPhone 3G and iPhone 3GS system interface uses Helvetica. As first noted by the always excellent DaringFireball, the iPhone 4 uses a subtly revised font called "Helvetica Neue." DaringFireball also notes that this change is related to the iPhone 4 display rather than the iOS 4 operating system and older iPhone models running iOS 4 still use Helvetica as the system font.
iPod models released prior to the iPhone use either Chicago, Espy Sans, or Myriad and use Helvetica after the release of the iPhone.
From http://www.everyipod.com/iphone-faq/iphone-who-designed-iphone-font-used-iphone-ringtones.html
For iOS9 it has changed to San Fransisco. See http://developer.apple.com/fonts for more info.
If you're doing programatic customisation, don't hard code the system font. Use UIFont systemFontOfSize:, UIFont boldSystemFontOfSize: and UIFont italicSystemFontOfSize (Apple documentation).
This has become especially relevant since iOS 7, which changed the system font to Helvetica Neue.
This has become super especially relevant since iOS 9, which changed the system font again to San Francisco.