No offence, usually said right before someone horribly insults you. It removes guilt from them and so they can say anything, however cruel without feeling remorseful.
Tony: "No Offence, but you look like you fell on your face when you were born."
What one says after realising one has said a slightly racist, sexist, homophobic or other comment in front of a person of the supposedly offended social group. The person will typically reply with "None taken"