My favorite Easter Eggs in video games are ones that are more than just an image or a line of dialogue. I like ones that go beyond a simple shout-out. Anyone can reference pop culture or a meme. Hell, people have established careers out of it. It takes effort to go beyond that.
My first example relates to a fairly-common Easter Egg: It's from Super Mario RPG: Legend of the Seven Stars. In Booster Tower, which is roughly halfway through the game, give or take, you come across a room with a curtained-off section at the upper floor of the room. Since this game is in an isometric perspective, you can literally go behind the curtain. What happens when you do this?
You get an awesome little Easter Egg in the form of Mario turning from his SA-1, Isometric 3D form into his 1985 Super Mario Bros sprite, complete with his original colors and a re-done 8-Bit-ish rendition of the Level 1-1 music!
Now, Square programmed all of Mario's walk animations, so you can move SMB-Mario around while still in 3D, with his 2D sprite. After a few seconds, you become small Mario and the music speeds up. Going back into the curtain at the upper floor plays the lost-life music from SMB, and you turn back into RPG-Mario.
This entire sequence will never be mentioned again, and it cannot be repeated.
Now, Square didn't need to do this. They took the effort to provide a nice little nod to Mario's past, and that's pretty awesome.
My second example is from a later point in the game: Monstro Town. This is a really cool town in the game where all of the residents are reformed enemies. Pretty neat. Strangely, there happens to be a locked door in the middle of town, with no way to open it. What lies behind it? Get yourself a Shiny Stone, and make sure your party is leveled up, because beyond that door lies one of the coolest bonus bosses in the history of the role-playing game genre:
Culex, Dark Knight of Vanda!
Culex is meant to be a personification of the Final Fantasy-style of boss, from his overworld sprite and his battle sprite being VERY different from how the rest of the characters in Mario RPG are rendered, to the four elemental crystals that enable Culex's attacks. To drive the point home further, the boss battle music for this fight is a variation of the music from Final Fantasy II (actually IV, but that is a whole other topic entirely), and the win music is that all-too-familiar fanfare that we all know and love.
Culex is a bitch and a half to fight, too. He is more powerful than the game's actual final boss by a significant amount, and you won't come remotely close to beating him without some planning and strategy. I suggest using the Lazy Shell armor on Peach, as that makes her into a healer that takes next to no damage, and it makes this fight a lot easier.
Your reward for slaying the Dark Knight of Vanda is an accessory called the Quartz Charm, which increases attack and defense by 50%, and also prevents its wearer from instant death attacks. It's a really nice item that would destroy most every enemy you come across. It's definitely worth the fight.
I love Easter Eggs like this one because it shows how dedicated the developers are not only to their past and their art, but to making Mario RPG the best possible RPG that it could be. It would be nothing to include a super-powerful fight against a palette swap of another enemy. Culex is 100% unique, unrelated to any other character in the game. He has an air of mystery around him, which is exacerbated after the fact because the door you went through to fight him disappears.
Sad to say, I spent a lot of time trying to beat Culex. When I finally did, the rest of the game was a cakewalk, as it should have been.
These two Easter Eggs aren't the only ones in this game, by far. There are still a few oblique references to other Nintendo games and some other bonus fights, but I'm not going to give those away. If you're interested, go and play Super Mario RPG for yourself if you haven't already!