There are three types of volcanoes: active volcanoes that have erupted recently and may erupt again, dormant volcanoes that are currently inactive, and extinct volcanoes that cannot erupt again. The document discusses the active volcanoes Kilauea in Hawaii and Arenal in Costa Rica. It also mentions the dormant Mount Fuji in Japan and the extinct Vesuvius volcano in Italy, which famously erupted in Pompeii.