There are likely some Japanese words you pronounce with an accent when speaking English, even if you speak Japanese. This is often preferable to using the Japanese word as it’s pronounced in Japanese if you’re speaking English, so you don’t sound pretentious like Ross on Friends talking about Ka-Ra-Te.
This list started off as words that you probably pronounce with an accent in English opposed to Japanese, however it’s really more a list of words that have been adopted into English from Japanese (and thus aren’t spoken with a Japanese “accent”, and are technically now English words).
I can only speak for American English, however a general rule for how words are pronounced is raising a middle syllable a pitch. For instance with the word “umbrella”, it’s “um-BREL-luh”. As another example “insurance” is “in-SURE-ance”. As a side note, this is typically the first syllable in southern states, where they say “IN-sure-ance” or “UM-brel-luh”. This raising of pitch often finds it’s way into Japanese words for English speakers. There is a pitch accent in Japanese, however if you aren’t familiar with the pitch of a word, your best bet is to speak it as flatly and steadily as you can without raising pitch.
English speakers will typically call this “Tera-YAH-key”. Sometimes it’s mispronounced further, like “Tera-yeah-key”.
English pronunciation of Teriyaki:
Japanese pronunciation of Teriyaki（照り焼き てりやき）:
In English, this is typically pronounced “Carry-oh-key”.
English pronunciation of Karaoke:
Japanese pronunciation of Karaoke（カラオケ）:
In English, this is typically pronounced “Toe-key-yo”.
English pronunciation of Tokyo:
Japanese pronunciation of Tokyo（東京 とうきょう）:
In English, this is typically pronounced “An-nuh-may”.
English pronunciation of Anime:
Japanese pronunciation of Anime（アニメ）:
In English, this is typically pronounced “Poh-key-mahn”.
English pronunciation of Pokemon:
Japanese pronunciation of Pokemon（ポケモン）:
In English, this is typically pronounced “O-rah-gah-me”.
English pronunciation of Origami:
Japanese pronunciation of Origami（折り紙 おりがみ）:
In English, this is typically pronounced “Nore-Ree”.
English pronunciation of Nori:
Japanese pronunciation of Nori（海苔 のり）:
In English, this is typically pronounced “Wuh-Sah-Bee”. On another note, most restaurants outside of Japan serve horseradish dyed with green food coloring (sometimes mixed with mustard powder or a mixture of a little wasabi). Wasabi is very hard to grow and too expensive for most restaurants out of Japan to keep in stock.
English pronunciation of Wasabi:
Japanese pronunciation of Wasabi（山葵 わさび）:
Rickshaw (from Jinrikisha)
In English, this is typically pronounced “Rick-Shaw”, coming from the Japanese “jinrikisha” (人力車), or “human powered cart”.
English pronunciation of Rickshaw:
Japanese pronunciation of Rickshaw （人力車 じんりきしゃ）:
In English, this is typically prounounced “Tie-Foon”.
English pronunciation of Typhoon:
Japanese pronunciation of Typhoon（台風 たいふう）:
In English, this is typically pronounced “Sah-Key”. It’s also not drunk quite as often as westerners would like to think, where the go to drink is usually beer（ビール）, watered down whiskey / ice (水割り), or shochu（焼酎）.
English pronunciation of Sake:
Japanese pronunciation of Sake（酒 さけ）:
In English, this is typically pronounced “Foo-Tawn”. In English this usually makes someone think of a fold out futon style couch, where in Japan it just means the mattress.
English pronunciation of Futon:
Japanese pronunciation of Futon:
In English, this is typically pronounced “Tem-poor-uh”.
English pronunciation of Tempura:
Japanese pronunciation of Tempura（天ぷら てんぷら）:
In English, this is typically pronounced “Ooo-Dahn”.
English pronunciation of Udon:
Japanese pronunciation of Udon（饂飩 うどん）:
In English, this is typically pronounced “She-Buh Eee-New”, or just “She-Buh”. Sometimes they’re referred to as “Sheebs”.
English pronunciation of Shiba Inu:
Japanse pronunciation of Shiba Inu (柴犬 しばいぬ）:
In English, this is typically pronounced “Kud-Zoo”. This stuff took over the southeastern United States, and seeing how much it grows is w i l d.
English pronunciation of Kudzu:
Japanese pronunciation of Kudzu（葛 くず）：
In English, this is typically pronounced “Kuh-Tah-Nuh”.
English pronunciation of Katana:
Japanese pronunciation of Katana（刀 かたな）:
In English, this is typically pronounced “Bahn-Zai”, which ends up sounding like a different Japanese word, 万歳（ばんざい）which can be translated as “hooray!”
English pronunciation of Bonsai:
Japanese pronunciation of Bonsai:
Not all words that came from Japanese are mispronounced, a lot of words have stayed for the most part intact. Here’s a group of words that sound (pretty much) the same in English and Japanese.
English pronunciation of Emoji:
Japanese pronunciation of Emoji（絵文字 えもじ）:
English pronunciation of Sushi:
Japanese pronunciation of Sushi:
English pronunciation of Shiatsu:
Japanese pronunciation of Shiatsu:
English pronunciation of Zen:
Japanese pronunciation of Zen:
English pronunciation of Koi:
Japanese pronunciation of Koi:
English pronunciation of Haiku:
Japanese pronunciation of Haiku:
English pronunciation of Miso:
Japanese pronunciation of Miso: