There don't seem to be many game specific design patterns, but one that we figured out while working on the oxygen series is applicable to almost every game ever created. We call it the tiers pattern.
Every game has tiers, the first on is the game. in the game tier, there exists data about the game itself, constants such as the levels to load, the defaults for character values and what characters you can have. There are variables too, such as screen positioning, volume settings etc, and then there is the game instance itself that loads up when you run the game.
Tier 2 is the session, this starts once you have commenced a game start / game load. Tier 2 contains variables for the number of lives, the current score, the inventory items, your upgrades, powerups, all the things that you would consider to be play session related.
Tier 3 is the instance tier, this is the in game dynamic instance that interacts with the World, there is one per entity in the world, they can all be different, they are initialised from the game tier and the session tier. Players and NPCs are initialised from the session and game tier.
How each layer interacts with each other is down to the type of game, but seperating your code into these layers helps in almost every game.
If you consider most adventure games, these tiers make enormous sense, what's not obvious is that they apply to games like tetris too. The tetris game doesn't contain much information other than the grid width and height and the descriptions of the shapes that can occur. The session is the game mode, current level, current score, and the instance is the player control device and the spawner that first creates the shape from the set of shapes defined for the game, then passes the shape to the player to control is within the context of the World (the grid and the shapes already laid down). The world is initialised from the Game and Game Session and instanced the player controller instance and the shape generator instance. The Game knew about the World object, and when the session was created, so was the World.