The Duel
If one dwarf has offended another, then that dwarf may challenge the other to a duel. If the other dwarf accepts, then the two will meet in a zone specified for such an event, where they will fight until one dwarf either yields, is knocked unconscious, or is killed. The winning dwarf gets a positive thought and the loser a negative thought.
In Adventure mode, you can also challenge others to duels.
Trial By Combat
If a dwarf must go on trial for committing a crime, they can have an opportunity to prove their innocence by fighting for his life against the accuser. The two parties will meet up in another such zone, where they will fight to the death. If the accused dwarf wins, he will be acquitted of his crimes.
Trial By Survival
A dwarf may also have a chance to prove his innocence by being banished to the wilderness (or caverns) for a set period of time. A zone would be set as an area that the dwarf would be "dropped off" at and would not be allowed to re-enter until his predetermined survival time has ended. In that time, the dwarf must survive against whatever may be out there. If the dwarf returns alive to the drop-off zone after his time is up, then he will be welcomed back into the community and acquitted of his crimes.
If the dwarf does not return to the drop-off point one week after his time is up, then that dwarf will be presumed missing until either the dwarf or the body is found.