For example, "flammable" and "inflammable" both describe an object that can easily catch on fire. I can also think of "ceased" and "deceased", both of which can mean someone or something has been brought to an end.
edit: Some people are including words that can also mean its opposite (like sanction or table), those are cool too! The more weird words, the better!
Sanction can mean a punishment or an authorization.
Came up in a DND game where a devil's contract said the players crossing the region would be sanctioned, or something like that. Players thought it meant they had permission, fine print said they would be punished.