The same is true for the shapes of incense burners, which range from a simple ceramic disk with a hole to elaborate and whimsical with figurines of all types. Also those are commonly sold in stores carrying traditional Japanese items and are, along with the assorted incense, a popular present or souvenir.
Incense is, of course, not unique to Japan, but is used all over the world. In Japan it is used quite commonly and as usual for Japanese things, comes in many refined forms. The most common shape is the incense stick, such as the cedar scented sticks from Nikko in the picture above. Also coils are a common sight (apart from the mosquito repellent type), but really, there is no limit to its possible shape.
Incense has an important place in Buddhist practice, and impressive incense burners can be found in every Buddhist temple compound. Incense can be purchased as an offering. Often, one can observe people fanning the smoke on afflicted body parts, hoping in its healing powers.
Whenever I burn some incense at home, I feel instantly transported back to Japan by its subtle fragrance.