Hello and Happy Easter. Just so you know a "video game easter egg" is something in a game that isn't meant to be or isn't important to the game and it's just there to make the game funny and so it can have something "extra". These easter eggs can be funny,weird,scary,boring,etc. So I'm just trying to say that there is no limit to a "easter egg".
5-Mario Paint-Title Screen
In Mario paint when the game loads it takes you directly to the title screen,and here you can press the letters in "Mario paint" and each letter does something "special".
4-Super Mario 3D World-8-Bit Link
In super Mario 3D World for the WiiU when you go to the first level of World-Star you will ride Blissy(she doesn't have a proper name but I like to call her Blissy) and after you get off of Blissy you will se a hidden wall that can only be open by lighting up the two torches on the wall. When you do light the two torches the wall will open appearing a cloud. Jump in that cloud. After that you will be sent to a big platform where you have to light up all the squares. At first it doesn't make all lot of sense,but when you finally light up all the squares the camera will zoom out showing a picture of Link(also a very famous Nintento character)and playing Links theme song.
3-Hey you Pikachu!-Angry Pikachu
Hey you PIkachu is a game where you used a mic to interact with the character in the game,which in this case is Pikachu. But some players decided to say Playstation and Pikachu would get really mad.
2-Super Mario 64-Yoshi
In Super Mario 64 if you were able to get 120 stars the cannon in the castle courtyard would open and shot you up onto the roof of the castle. There you would meet Yoshi and he will give you 100 lives and a cool sparkle whenever you jump. It's just a pity that you can't ride him:(.
1-Pokemon X&Y-Lumiose Ghost Girl
And finally the best(in my opinion)Nintendo easter egg. In pokemon X&Y if you go to Lumiose City and go to a specific apartment and go up the elevator a Ghost Girl will appear and thats all she does. She doesn't really have a purpose but who knows maybe in the near future she will.
By-American Nintendo Boy :P