From Nookipedia, the Animal Crossing wiki
The Nintendo Set is a collection of items in the Animal Crossing series that first appeared in Doubutsu no Mori and contains objects found in other Nintendo games. The set started off with just four items in Doubutsu no Mori. In Animal Crossing: Wild World the N Logo and G Logo were replaced by the Triforce and Metroid. Animal Crossing: City Folk added the Yoshi's Egg, Banana, Triple Shells and Kart, bringing the total number of items in the set to eight. The Banana was replaced by the Triple Bananas in Animal Crossing: New Leaf and saw the addition of the Blue Falcon, Pikmin, S.S. Dolphin, Virtual Boy, and Wii Balance Board, bringing the set to thirteen items total. The Blue Falcon and Pikmin existed in both Wild World and City Folk, and the S.S. Dolphin was distributed as DLC in the latter, but none of the items were considered part of the set in those games.
Doubutsu no Mori, Doubutsu no Mori+, Animal Crossing, and Doubutsu no Mori e+
Animal Crossing: Wild World
Animal Crossing: City Folk
Animal Crossing: New Leaf