Yokan ようかん
Yokan - sweet jellied red bean paste Yokan is or was mostly known as Japanese typical desert outside of Japan for a long time. Nowadays there are many other alternatives, but it must be still of the best seller. If it is too sweet and cruntchy for your favourite why don't you try Mizu-Yokan which is slightly mild.
Senbei せんべい
Knead rice powder with water and grill or fry. The crispness is very important element for Japanese senbei. Chinese senbei is made on the pan and bit like pancake.
Okaki おかき
Ingredient is rice cake "mochi" which is made from steamed and pounded glutinous rice. Okaki is made with these mochi which is cut in various small forms and grilled or fried. I see it often in European supermarket. They are not "made in Japan", but taste surprisingly identical.
O-Manjuh お饅頭
Traditional main contents are red bean paste and dough which is made with flower. Tehre are many variations, but usually sweet stuff such as red bean paste "anko" is stuffed into the dough and steamed. Is is said that manju is brought from China together with buddhism in the 14th centry.
Kasutera カステラ
Kasutera does not sound like Japanese, does it? Portuguese should have brought cakes made with wheat flour, butter and eggs which Japanese never had, in 16th century. Usually this kind of old sweets are also categorized as Japanese sweet as they have long enough history.
Dango だんご
Rice or grain powder mixed with water, knead and steam or boil. Some will be grilled and eaten either sweet or salty with soy sauce taste.