1 - Manga and Anime
Manga and anime are basically Japanese comic and animated films. The exact time when first manga appeared is still a question. Some say first manga appeared in 12th century in the form of scrolls, but others say its truly first appearance was actually in 18th century. Manga has become so popular, not only in Japan but around the world, for example: Naruto, One Piece, Bleach, .etc... On the other hand, Anime's first appearance seems to be in 19th century. Most anime series come from manga. The more famous a manga serie is, the higher chance it will get its anime adaption. Of course there are many other standalone anime films, probably the most noticable anime films or movies come from Studio Ghibli. Nowadays we can say manga and anime are the two most popular Japanese words used in English.
2 - Karaoke
"Karaoke" is actually originated from Japan. In details, Karaoke is a form of entertainment of Japanese people, after work, many people often go to Karaoke bars to sing and have fun. If we split the word "karaoke", we will have "kara" ? which means "empty", and okesutora ?????? which is actually Katakana word for "orchestra". So, by combining both words we have "empty orchestra"?... Well in any cases, karaoke is what people around the world do, not just Japanese people like the old days. No wonder why "karaoke" is a popular Japanese used in English, too.
3 - Japanese words for Japanese cuisine
Japanese culture is so "magical" that it spreads all around the world, so too the cuisine. Among Japanese dishes, there are several common Japanese words used in English. For example: Sushi - a super popular Japanese dish made of rice part (shari) and another ingredient (neta), neta ingredients can be vary, however they are mostly seafood. In case of raw fish slices, they are called "sashimi". Ramen - Japanese noodles said to be originated from China, normally served with pork, green onions, soy sauce or miso, seaweed. Sake - Japanese wine made of fermented rice. Of course there are much more dishes to talk about, but for now, these 3 are the most popular Japanese words used in English.
4 - Samurai and Ninja
Probably we are so familiar with these words since they are popular Japanese words used around the world, especially on entertainment industry. "Samurai" refers to Japanese swordsmen or warriors exist in feudal Japan era. Samurais are famous for their sword skill and their unbending will of steel. In Japan they have "Bushido" or "the Way of Samurai". They are also known for their loyalty, that might be the reason why exiled or samurais who don't have master to serve are called "Ronin". On the contrary, "Ninja" refers to Japanese assasins, who normally are pictured as the guy who wear black hooded clothes and do the assasination. If you already read Naruto then this should be familiar to you (except the ninjas in Naruto are different from real-life), and of course they also have "Ninjutsu" which is "Ninja Arts".
Source: blog.akirademy.com