Ask a grammar geek about the double negative, and you’ll invariably hear about its long and noble heritage in the English language, from Chaucer to Shakespeare, up to the 18th century, when it all but died at the hands of overly zealous, systematizing Enlightenment linguists.
Whatever its history, however, the current view of most pragmatic writers is that the double negative should be avoided, if for no other reason than that a crotchety old English teacher might discover it and try to publicly humiliate them for using it. In many cases, people will read a double negative as if it equals a positive. One exception, as the American Heritage Dictionary of English Usage points out, is the expression, “You ain’t seen nothing yet,” which any reasonable person would admit is the equivalent of “You haven’t seen anything yet.”
The problem with the double negative is probably more social than grammatical. Sadly, many people are quick to make assumptions about the education, intelligence, or even social class of someone when they hear him or her use a double negative such as “I didn’t do nothing last night,” or “I couldn’t find nothing at the store.” My advice is to avoid it, especially in writing or when standard spoken English is expected.
One form of a double negative is also an example of the rhetorical figure litotes, or the use of understatement by denying the contrary. (e.g. She is not unkind.)
You can read more about double negatives at the American Heritage Dictionary of English Usage.
Thank you, Marla, for the question and the examples!