How Do You Say 'Thank You' In Japanese?

There is more that one way to say 'thank you' in Japan and it depends upon the particular area at which you are at particular time. One of the most famous term that is used to convey the idea of 'thank you' is 'Arigato'. Sometimes some people exactly want to convey the idea of thanks but they have their own way to convey the same idea. The term is ''Arigato gozaimasu' and when you translate the term exactly in the English language it stands for 'act of thanks not ended'.
      
Some other areas of Japan have their own way to convey the same idea and when you are in Osaka you can use the word 'ookini' while some parts of Japan use the term 'Domo Arigato' to convey the idea of thank you.

All of Vickys answers are correct. You can never go wrong with saying "Doomo Arigato Gozaimasu" Roughly translated to "Thank You Very Much".

There are 4 ways to say it (as far as I can think of)

どうもありがとうございます(doumo arigatou gozaimasu)

ありがとうございます(arigatou gozaimasu)

ありがとう(arigatou)

どうも(doumo)

''Arigato gozaimasu'  Arigato

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Hi yuri nice meeting you and thanks for dropping by have a nice day

Domo arigato mr roboto

I think that it is domo arigato

DOMO ARIGATO MR.ROBATO DOMO domo *beep* *beep* *beep* DOMO domo *beep* *beep* *beep*

Eireannach is correct, but the pronunciation is not obvious.  "Domo Arigato Gozaimasu" is pronounced:
  Doh moh ah ree gah toe goes aye ah mus (the last "u" is silent)  
But, as in the USA, there are regional accents, Rural Japanese might pronounce the "u" at the end.  The real key to making it sound good, though, is to avoid putting any accent on any one syllable - pronounce all the syllables with the same emphasis.  In common conversation, one would rarely use all three words and, in fact, any one of these can be used alone to say "thanks".

M3tal your retarded. Its chang ching pow chong. XD

'Thank you' in Japanese is said as 'Arigato.' Pronounced, (Are-ee-gah-toe)

Arigato=thank you

I am half Japanese so this is true!
Thankyou in Japanese is "Aligato"

(most polite)Doomo Arigatou gozaimasu
(informal)Doomo
Arigatou

Domo arigato mr roboto...

Ching chang chong pow