One could say that Japanese is a very absorbent langange, meaning that it has taken, appropriated, and made its own countless number of loan words, or gairaigo as they are known in Japanese. Most gairaigo entered the language from Chinese 1500 years ago, with a certain amount also coming in slightly more recent times from Portugese Jesuit priests (tempura, for example) and Dutch traders (eg. kaban, meaning bag, satchel, or briefcase).
Most of these words have long been assimilated into the language to the point where their origin, at least to an outsider or non-native speaker, is obscured. However, it is the more recent English imports, like waishatsu (business shirt, not necessarily white), pasokon (personal computer), conbini (convenience store), or tsuaa kondakutaa (tour conductor), that get the most attention these days (popularized as either “Japlish” or “Engrish”), often because their meanings — to say nothing of their pronunciation — are at odds with that of the original word (manshon — ahem, “mansion” — for apartment building is one of my favorites).
If I may borrow an economics analogy, we could say that with respect to the English and Japanese languages, it is English that enjoys a considerable trade surplus. Japanese words that have entered into the English language are few and far between, and most of them directly refer back to some item or element of Japanese culture, eg. futon, origami, sushi, kimono, tofu, sake, zen, etc. However, there are two words in English that entered the language from Japanese whose entry I find curious and amusing, in part because not only are their meanings somewhat related, but their etymologies are mutually resonant as well. These two words are tycoon and honcho.
According to Dictionary.com, tycoon has a particularly fascinating history of how it entered into English, going back to Commodore Perry in the 1850’s:
Tycoon came into English from Japanese, which had borrowed the title, meaning “great prince,” from Chinese. Use of the word was intended to make the shogun, the commander in chief of the Japanese army, more impressive to foreigners (his official title shgun merely meant “general”). It worked with Matthew C. Perry, who opened Japan to the West in 1854; Perry carried out his negotiations with the shogun, thinking him to be the emperor. In fact, the shogun did rule Japan, although he was supposedly acting for the emperor. The shogun’s title, taikun, was brought back to the United States after Perry’s visit. Abraham Lincoln’s cabinet members used tycoon as an affectionate nickname for the President. The word soon came to be used for business and industry leadersat times being applied to figures like J. P. Morgan, who may indeed have wielded more power than many princes and presidents.
Honcho, which comes from the Japanese hanchou and means “group leader,” is a more recent addition to the English language, again resulting from American involvement in Japan, this time from the post-World War II occupation of the nation by the Allied Powers.
There are a couple of words or phrases in use in English that have occassionally been traced back to Japanese, though the etymology is inconclusive or at the very least fanciful: hobo, and hunky-dory (as in the expression “Everything is hunky-dory.”).
There are some who wonder if the word hobo, meaning “One who wanders from place to place without a permanent home or a means of livelihood” (American Heritage), whose etymology has always been listed in dictionaries as “of unknown origin,” might be from the Japanese word houbou, meaning “here and there”. But this seems to be pure speculation, and speculation not shared by too many at that. Merriam-Webster seems to think hobo has a purely American origin.
According to the Word Detective, there are some that believe that hunky-dory originated from a street popular among American sailors in the 19th century in Yokohama named “Honcho-dori.” The story is fascinating, but unfortunately the facts don’t add up so neatly. See this thread at Phrase Finder for more.

