The F-Zero series has Easter Eggs that appear in specific games from a different Nintendo series. They have mostly appeared in Mario games. They also appeared in Kirby games and Animal Crossing games.
In the 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 by completing a specific criterion appears as an Easter egg. 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. Captain Falcon also appeared as a Mario Costume for the Mystery Mushroom usage in Super Mario Maker. While it was temporarily possible to unlock Captain Falcon via 100 Mario Challenge under one circumstance before the Nintendo Network Shutdown, it can always be done via amiibo.
In almost every Animal Crossing game, you can get a Blue Falcon as 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.
In Yoshi’s Woolly World, scanning the Captain Falcon amiibo can unlock the Captain Falcon design for Yarn Yoshi. This also works in Poochy & Yoshi’s Wolly World for the Nintendo 3DS.