A famous example by Sperber & Wilson shows the context dependency of conversational inferences:
He: Will you have some coffee?
She: Coffee would keep me awake.
Depending on whether one surmises that she would like to stay awake, one can infer either a positive or negative answer to whether she would like some coffee.
The April 7, 2014 issue of the “Zits” cartoon gives us a new illustration: