People celebrate many festivals in Taiwan. A visitor can find them very enjoyable and colorful. Workers are glad to get the holiday. The traditional festivals also help to keep Taiwanese culture alive in the modern world. Because they are set by the lunar (Moon) calendar, the dates change every year in the western calendar.
As well as the normal Chinese festivals, there are also local Taiwanese ones. For example, Matsu Goddess of the Sea, is very popular in Taiwan because of the importance of fishing. Therefore around the island, you may often find a festival to celebrate her. Another example is the City God of Taipei whose birthday is celebrated every year. If you go to Yenshue there is a particularly crazy fireworks festival which takes place at the same time as the Lantern Festival. People wear protective clothing while rockets and fireworks explode around them. Visitors come from around the world to participate. Every year some people are hurt so if you do go, wear protective clothing (including a helmet!).
There are also aboriginal and modern cultural festivals. If you find yourself in an area where there are many aborigines such as the east coast, you may be lucky to see one. Their harvest festivals are especially popular. There are many varied modern festivals including the stone sculpture one in Hualien and the Children's Folklore & Folkgame Festival.