Well, I might sound silly and excessive but I just feel the urge to contribute my two cents to this funny discussion.
At school, in English class, we were tought that a double negative is incorrect. You don't want to say "I don't know nothing", "Don't sign nothing". You say, instead, "I know nothing/ I don't know anything" "Sign nothing/Don't sign anything."
These, I've always believed, are basics.
Yet when you come to live in the English-speaking country, as it happened to me, people are not going to always speak the correct English for you. So, I believe, we, non-native speakers, should be aware of such expressions to exist and understand them. But we don't have to use them...
And indeed -- "Don't sigh nothing" sounds awfully clumsy even for my foreign ear.