F-Zero series have Easter Eggs that appear in specific games belonging to a different series created by Nintendo. They have mostly appeared in Mario games. They also appeared in Kirby games and Animal Crossing games.
In Mario Series, you can find a Blue Falcon as a trophy in a specific location in Super Mario RPG: Legend of the Seven Stars. In Mario Kart Wii, a Blue Falcon that you can unlock for completing a specific criteria appears as an Easter. The Blue Falcon, Big Blue, and Mute City appeared as Easter Eggs in Mario Kart 8 and Mario Kart 8 Deluxe and so did several music pieces in F-Zero.
In almost every Animal Crossing game, you can get a Blue Falcon as a furniture. You can interact with it in your house. There is a requirement for each different game to get this furniture. In New Leaf, for example, you can get the Blue Falcon via Fortune that you receive from eating Fortune Cookies.
In Kirby Super Star, the Falcon Helmet appears as a F-Zero Easter Egg treasure in The Great Cave Offensive Mode.