Not to be picky, but I don't see a good clear statement of the problem of double negatives here.
The way English grammar is set up, using a double negative should make a positive:
"I can't not go" = "I have to go"
"Well, it doesn't not work" = "It works! (albeit not as we planned)".
But many English users treat double negatives as if they are negative:
"I'm not never going"" = "I'm never going"
"There ain't nothing wrong" = "Nothing's wrong".
This is annoying to people who like to keep the language neat and unaltered from the Queen's English. Double negatives are often considered to indicative of a lower class upbringing and a poor education. There is some truth to this, but not as much as the grammar police would have you believe.
Of course, some double negatives are perfectly acceptable in English even to express a positive. Even Kelsey Grammer can get away with utterances like "I will never, never do that" or "no, no, no!". Repetition of a negative for emphasis is perfectly fine.
In Spanish, and many other languages, double negatives are fine. They are not positive nor necessarily used for emphasis, they are simply a way of speaking.
As a side note, in African American English it isn't uncommon to use a triple negative; "Nobody don't never do that". Correct under any grammar system!