As I explained to my friend once, there are many ways to play a fighting game as to avoid monotomy. Granted if it is a deep fighting game like MK Deception, or Tekken 5 you should have no problem. However, if you are looking for a little spice in your love life to fighting games try these styles of games.
Player elimination: for 2 players
When heading up one on one with someone in a fighting game, you must not simply fight once, for to do so would be in error. You must fight several times. Also a true fighter must be skilled in every player not just one. So in order to accomplish these two things what must be done is this. You must fight and then the winner keeps his character, and the other may not choose the character he had when beaten, nor if the one who prevailed should lose, may he choose that character, simply put when a character is beaten he may not be chosen again by either player, you go on like this until there are no more characters to choose from.
Another variation of this is that a player cannot pick fighters he has lost from, but say his opponent loses with Sub-zero, he may yet still choose subzero for himself. Thus the person who has no more characters left loses.