Back in grade school whenever we played a game of Tic-Tac-Toe (X's and O's) and the result was a tie, we would call it a "Cat's Game." I've never heard this term applied to a tie in any other circumstance and was interested in where this term came from and why it seems to be unique to Tic-Tac-Toe.
I always took it as a sort of dismissal of the game. When you think about the games that a cat would play, such as batting around a toy, or chasing it's own tail, there is no win condition. So basically it is saying "That is a game that served no purpose".
Apparently on the broader scale tic-tac-toe has always had a connotation with cats in many different cultures, here is an interesting snippet from a podcast discussing the topic http://www.waywordradio.org/tic-tac-toe-cats-game/
The "best answer" on Yahoo regarding this subject refers to it as a "cat trying to catch its tail." The analogy is that a cat won't win the game of trying to catch its tail, and you can't win a tied game of Tic Tac Toe.
This seems plausible, but then again, I've seen plenty of cats catch their tails.
Another source suggests that Tac spelled backwards is cat, and cats scratch. And, since the game is a scratch . . .
Completely winging it here, I'm going to suggest that Tic-Tac-Toe is typically a childrens' pastime, so it's natural to associate it with The Cat's Cradle Game (a "game" which nobody "wins").
It's worth noting that many/most children are fiercly competitive. If two children are playing Cat's Cradle and it "goes wrong", one might well start complaining vociferously that it was the other's fault, and thus that he somehow "lost".
It's easy to imagine a nearby adult stepping in and defusing the situation by pointing out that Cat's Cradle isn't a "win/lose" sort of game. It would thus be quite natural for the children to figuratively refer to that "no winner" game later, when Tic-Tac-Toe ends in a draw.
The earliest reference I can find for this usage is from 1952, and implies it probably wasn't a "recent coinage" at that time.
I always figured it was almost a method of keeping score of the tie games, i.e "we were 1 and 1 and then tied this game, so who gets the point? i guess the cat? alright so the cat gets the point for that round, chalk it up as one of the cat's wins, or it was a cat's game"