FedEx, Airborne and UPS all deliver to more than 200 countries — essentially the whole world, with a handful of exceptions. Other major companies, such as DHL, also offer international shipping services. Regional companies are a different matter; some deliver to selected overseas locations, while others don't provide any international service.
Keep in mind that international delivery service can be much more expensive than domestic service. (A notable exception is USPS service to overseas U.S. military APO and FPO addresses, for which its domestic rate is charged.) Shipping services often guarantee next-day or second-day delivery to major European, Canadian, and Asian cities; however, they do not always guarantee the same level of service to more remote locations.
Shipping services must obey each country's laws and regulations. Remember: A product or document that is perfectly legal in the United States may not be legal in another country. It's also important to note that there are a few countries, including North Korea and Iraq, where shipping companies either cannot or will not deliver.