Travelers will probably be a bit annoyed at not finding many public trashcans in Japanese cities, especially considering the number of vending machines in urban areas. However, the reason for this is actually quite interesting. A domestic terrorism attack in 1995 resulted in many urban areas removing public trash cans. However, it isn't really considered that much of an issue since littering is, culturally, not something that you do in Japan.
Most people in Japan will simply store their wrappers in their bags and bring them home with them to throw away. In recent years, trash cans have started to return, but you'll often see them locked up during public events or holidays.