Originally posted by: anphorus
It is my understanding that "Domo Arigatou" means "thank you very much" as either Domo or Arigatou on there own can be used as thank you. "Domo" means both thank you and hello.
This is how I have understood it to be. Ranking the grade of "thankful-ness" from lowest too highest.

Domo
Arigatou
Domo arigatou
Arigatou gozaimasu
Domo arigatou gozaimasu