It is a popular dish, and is often eaten on special occasions (or, you might order cuye at a restaurant to try to impress someone). Cuye asado is the favored preparation in the sierras, where it is roasted on a spit, similar to a rotiserrie chicken. I tried cuye with my host family on Father's Day.
I was definitely a bit hesitant to try cuye, but nevertheless excited. It was definitely yummy, and many people compare the flavor to chicken, but it was a little bit too greasy-tasting for me. Nevertheless, being able to share that experience with my host family, and being able to try such an important food was a special moment.
Cuye can be prepared in many ways. It is usually asado but can also be frito, and is usually served as a cuye entero o la mitad. Be prepared... it's not like you are ordering a hamburger patty or a chicken breast. You get the whole (or half) animal!
Cuyes play an incredibly important role in indigenous medicine, used during limpias (cleansings), in which a curadero/a (healer) will rub the cuye all over your body. In the process of rubbing the cuye over your body, it absorbs your ailments and bad energies. The curadero/a then examines the cuye to see wrong in your body, and they can then give you a diagnosis. This practice is alive and strong in many parts of Ecuador today.