In dialogue, you can sometimes choose to Brawl with someone. A brawl is a hand-to-hand fistfight between you and another character. Neither of you can die during this fight. However, if you use a weapon or cast a spell, the fight will turn into a live combat and you may be guilty of a crime.
Tip: Khajiit do well in brawls, as their increased unarmed damage allows for a quicker end to the brawl and an upper hand against more heavily armoured NPCs.