There are many Japanese words that have been incorporated into English. Among these, words related to traditional Japanese culture make up the majority.
Bonsai, ikebana, origami, and haiku are well known. In entertainment there are kabuki, noh, and bunraku. In sports there are sumo, judo, karate, and aikido.
The others include, Zen, Shinto, shiatsu, tatami, futon, kimono, obi, geta and geisha. There are also many words that relate to history: Mikado, shogun, daimyo, samurai, ninja, hara-kiri, and kamikaze. Since these are things unique to Japanese culture, no suitable English words are available, therefore it seems that these words have been incorporated into English.
There are also many words taken from contemporary Japanese culture.
Manga, anime, cosplay, otaku, and recently kawaii have spread throughout the world. More words related to daily life are shinkansen, onsen, karaoke, sudoku, tsunami, shiba inu, yakuza, sensei and sayonara. Due to the world-wide Japanese food boom, food related terms are also spreading.
In cuisine, sushi, tempura, sukiyaki, sashimi, ramen, teriyaki, tofu, edamame, and umami have become English words. Words for condiments used include, miso, wasabi, as well as cha and sake.
Conversely, some words such as tycoon and rickshaw which have become English words, are not much used in contemporary Japanese. It seems that along with the advance of globalization, from now on more words relating to Japanese culture will be incorporated into English.