Regardless of the fact that it is cardboard, the Bible does say to avoid the appearance of evil, like beads said.
Why does one have to play with a Ouija board in the first place? Heck, what's wrong with a good game of Clue, or Monopoly, or Chess, even? But, hey, I guess that's Satan for ya; he is the father of lies. I, myself, am glad to have never seen such a board.
To Tom: What you say is true; you could probably contact an evil spirit in a bottle of water, a bottle of perfume, or a bottle of gin. Regardless, the game was designed, I don't care for what purpose, to have fun through meddling with evil spirits. Satan uses many things to deceive people, and the Ouija board could be considered one of his games that non-believers can easily succumb to.
Frankly, people, if you think otherwise, lemme' know. Even if you play with no desire to contact such evil spirits, or you play with the Spirit of Christ inside of you, avoid the appearance of evil! You shouldn't be near it! To put it in another perspective, pretend you are playing teh game, and Christ is with you. He is standing there beside you, smiling, watching you. Would that not make you feel uncomfortable? Well, let it make you uncomfortable, for that Spirit of Christ is in YOU! Your body is a temple of the risen Lord our God, and we should not be toying with anything that would influence us in any other way! Honor God in what you do, on the outside, and the inside, for even though you may think "Aw, it's just a game," no, it is not just a game.