Two expansion sets have been published for Sid Meier's Civilization III: Play the World, and Conquests.
Play the World added multiplayer capabilities, eight new civilizations and some new units to the original release.
Conquests offers nine more historical scenarios, ranging from Mesopotamia to WWII in the Pacific. Many of these scenarios have resources, improvements, wonders, music, and even government types that are specific to the scenario, especially the Mesoamerican and Sengoku Japan campaigns.
The stand-alone version is Civilization III: Complete Edition, which includes the two expansions and several patches. (This version came after Civilization III: Gold Edition and Civilization III: Game of the Year Edition.)
Source: Wikipedia, "Civilization III", available under the CC-BY-SA License.