Forests often play a huge part in my own stories, but whether or not they will in yours will depend on the story you are writing. Most of my forests fall under everyone's perception of a forest, which is often classified as a temperate forest, but there are two other types of forest that can make for great story settings.
The temperate forest is the kind of forest that occurs in Eastern North America, and much of Europe and Northeastern Asia. There is great variation between the seasons in temperate forests, and they can be further classified by the amount of rainfall they receive.
Boreal forests are cold forests. They are also called taiga and cover much of Alaska, Canada, and Siberia. The growing season is very short and the winters are very long.
Tropical forests have the greatest number of species compared to temperate and boreal forests. They have high rainfall and only two seasons, rainy and dry. These are the rainforests that run along the equator. The Amazon in South America and Congo in Africa are the two most thought of.