On the back of the game box it will tell what form of multiplayer the game has.
Single Card Multiplayer - You only need one game and all other players download it. Mario Party, Mario Kart and I believe the new Ravin Rabids is this way. Sometimes game play will be somewhat limited - like character selection may use default characters, or boards will be limited.
Multi Card Multiplayer - Every player is required to have a copy of the game to play. Such as Pokemon Diamond and Pearl.
Some games do both forms. I believe Mario Kart does both forms but having multiple carts will allow all players to chose their characters.