Nintendogs
The very first virtual dog keeping simulator on the Nintendo DS console (or any console I guess), this is a very unusual game Nintendo published. The goal of the game is to choose some dogs to own, based on what version of the game you own, and then look after them by teaching them tricks, taking them out on walks and taking part in dog show type competitions. It makes heavy use of the touch screen and microphone, with the Mic used for walks, some tricks and cleaning the dog, and the microphone used for commands to tell the dog to do tricks.
You can also get many bonuses in this game, such as toy Mario Karts and the like by going on walks and finding the items along the way. There is also a mode using local multiplayer (not wifi though), but I cannot comment on that.
Oh, and regardless to the pathetic rumours and joes found on the Gamespot forums, there is no game called Nintencats planned, even though I personally prefer cats to dogs.