Phones that use SIM cards need the information on the SIM card to utilize cell phone networks, so it is not possible to make standard phone calls without one. It may be possible to use some voice-over-IP services on a wireless Internet connection on a phone without a SIM card.
The SIM in SIM card stands for Subscriber Identity Module. The SIM card contains information about the user and their phone number, address book and other information. The phone itself usually does not contain this data and cannot authenticate itself to a cellular network on its own. An exception to this rule are so-called "global phones" intended for use on CDMA networks that also include a SIM slot for compatibility with GSM networks. These phones store information about their CDMA authentication internally and do not need a SIM for calls on those networks, but do require a SIM for calls on a GSM network.