Your grade school English teacher told you repeatedly that you couldn’t use more than one negative word in the same sentence. In Italian, though, the double negative is the acceptable format, and even three negative words can be used in a sentence:

Non viene nessuno. (No one is coming.)

Non vogliamo niente/nulla. (We don’t want anything.)

Non ho mai visto nessuno in quella stanza. (I didn’t see anyone in that room.)

In fact, there is a whole host of phrases made up of double (and triple) negatives. The following table includes most of them.