All iPhone models, with the exception of the iPhone 4 CDMA, use SIM cards, as of 2015. The SIMs used in iPhones vary between mini, micro and nano, depending on the model of the phone.
The mini SIM is the SIM card many people are familiar with and is often simply called a SIM card. It is the largest SIM card available and is now being phased out in favor of smaller SIM cards. iPhones using the "regular" SIM cards are the original iPhone, the 3G and the 3GS. The iPhone 4 and 4s use the micro SIM and the 5, 5C, 5S, 6 and 6Plus use the nano SIM.