Calling American phones numbers with a cell phone while travelling internationally is not free. In fact, using American cell phones to make calls from other countries is generally considerably more expensive than using a landline or a calling card no matter what location or type of phone is being called.
It is possible to place and receive calls from cell phones while out of the country, but dialing protocols vary by country and charges can be quite high. Calling from landlines or investing in an international calling card may be worth the slight lack of convenience.
Most major cell phone carriers have partnerships with foreign carriers where the foreign carrier takes over service while the user is within the country's borders. This is called roaming. Most cell service providers do not have roaming as a default feature, however, and it's necessary to activate roaming service through the wireless carrier before leaving the United States.
Some service providers block international calls on request. This may also be a wise option to activate, because both incoming and outgoing calls to a cell phone in a foreign country incur charges even if the calls are not answered. Calling toll-free numbers from international locations also incurs charges.