Have you ever played Monopoly? How about Hogopoly, where all the pieces are pigs? You get to create the characters and name them.
Chess? How about Mess? It's like chess, with kings, queens, rooks, bishops, knights, and pawns--but you decide the rules and mess things up.
Scrabble? How about Scramble? After a player puts his letters on the board, the next player scrambles them to create a made-up word.
Trivial Pursuit? How about Life-and-Death Pursuit? Your answers to a series of trivia questions can mean that you live or die (in the world of the game, of course).
Try inventing your own game. Come up with a fun name, write down the rules, and create a game board and pieces with paper, cardboard, markers, or other material--or even on the computer once the power comes back on!