This is more of a glitch, but it's too rad not to include. For years, the Master Hand was just the unlicensed Glover ripoff that served as the boss of the Smash Bros. series. It wasn't until 2008, the year of Brawl's release, that a method was discovered that let you play as MH in Super Smash Bros. Melee.
Here's where the "easter egg" and "glitch" part get mixed up. You have to plug your controller into the third slot and hold down certain buttons to pick Master Hand, but it's probably not intentional. The Smash Wiki I linked calls it a glitch because it basically involves skipping the character select screen, after which your fighter defaults to Master Hand. Though Master Hand is perfectly playable, complete with a moveset, winning with him/her/Glover will crash the game because MH has no win pose animation. Despite these drawbacks, and the fact that it's a programming error, I stand by my previous assessment of calling this a radical easter egg.
Goldeneye was already full of unlockables, but since 1997 the internet has exhumed a ton of other oddities within the game. Secrets like Line Mode, the unfinished Citadel level and playable Sean Connery have captured the imaginations of permanent 11-year-olds everywhere, but the craziest Goldeneye discovery came in 2012. 15 years after your childhood friendships were destroyed by Oddjob, a dedicated forumgoer dug into the code within the game and found an emulator for the ZX Spectrum computer. For those not familiar, the ZX Spectrum was kind of like a British Commodore 64. For those too young to know what those words mean, imagine like a big bulky version of an iPhone 3G. Developer Rare made a ton of games for the Spectrum back in its day, and ten of their titles were included on the Goldeneye cartridge along with the emulator.
As the story goes, developer Rare was probably tinkering around with the idea of emulation on the N64, and used their own catalog of ZX Spectrum titles as a test. Maybe they were testing out emulation so they could use it for the playable Donkey Kong arcade cabinet in Donkey Kong 64, or maybe working on emulators was the mid-90s version of avoiding work by puttering around on Reddit. Rather than yoink the stuff out of the code of Goldeneye before they released it, Rare just disabled the Spectrum emulator and left it on the cartridge. If you want to play piping hot titles like Jetpac and Gunfright on the Nintendo 64, you have to run Goldeneye in an N64 emulator and then run a special patch to then run ZX Spectrum emulator. It's probably way simpler to just run a Spectrum emulator, but if there was any fun in that you would have done it already.