Chilies are used as a major spice in numerous cuisines, both New World, Old World, and Africa, as well as Asia.
One interesting note: In general, the closer to the equator a country lies, the "hotter" the food will be.
In terms of Western cuisines, BDL pretty well summed it up, with the noteable absence of the American Southwest, where chilies are king.
Fusion cuisines, such as the Creole cooking of the American gulf coast also tend to use chilies extensively. As do many Carribean cuisines. Jamaican jerk dishes, for instance, can blow the roof off your mouth.