Mochi: Japanese. The steamed rice is pounded into paste and molded into the desired shape. Also Koreans do something similar.
Rice noodles: Uncooked rice is ground into flour and then rebuilt into a new shape.
Rice paper: Vietnamese thing. Same idea, different shape.
Puffed rice: Popular in many countries.
Rice crackers: East Asian, cooked rice flour
Arròs negre: Spanish thing, squid ink + rice
Nian gao: Chinese new year cakes
Arancini: Italian rice balls
Appam: South Indian pancakes
Jiuniang: Chinese fermented sweet soup
There are also many alcoholic beverages made of rice.
See also: OMG, there are so many