On the parallel of fourth wall, some classics had hidden elements a few didn't notice before.
Super Mario Brothers series -
Lost World levels were called (-) or minus worlds, essentially if you played the game normally you would actually miss these. But if you were persistent, and explored they could be found in the most abstract places.
In World, there were hidden levels that could be unlocked by finding keys to unlock pathways throughout Star World. (and a hidden ending)
Paper Mario - There are so many goodies they can only be found by obtaining every skill with your buddies.
Legend of Zelda -
From obtaining all hearts, to all weaponry, or even finding hidden ways to knock out baddies.
The flute can defeat various critters (but the Japanese version of LoZ 1 used the console's built mic for sound fx) *same concept the ds and 3ds also uses now.
Ocarina of Time -
There are many hidden side quests, the game can be pushed to many limits. Beyond the hillside of Hyrule, helping people along the way (and some of the creature folk) may yield rewards.
Majora's Mask -
Every mask has a story, but each one also yields untapped secrets. Some of them also give you unique powers versus elements within the in-game hub world. But be advised that Moon can still fall anytime you make a mistake along the way.
A fun crossover some didn't notice before - In SMB3, there was a hidden flute that could be used to teleport you across the world maps. The note played was from Legend of Zelda. Once used, Mario or Luigi could continue their quest across interconnected pipe worlds, as long as they were on the same path way.
Sonic The Hedgehog -
Listen to each level's bgm, because they actually reveal the timing behind various obstacles or platforms that get in your way. There is a hidden rhythm within each level, included the later Egg Battleship in Sonic III, Adventure, Heroes and beyond!
Colors - Red Rings
Although these oddities yield rewards what do they actually unlock? To be honest its still a great mystery because these will return in Sonic Lost World and may connect with that games' quest.
Metal Gear Solid Series -
From past to present, this series tosses a ton of weird and bizarre hidden elements. MG (the US NES version) was in fact not the original MG title, the first was in fact on the MSX (a pc based console). The version we played was actually a revamped and lost SNK licensed title. But with the namesake, the game was a top down shooter, with some occasional side scrolling elements.
MGS4 actually took a nod from a classic Kojima game called Snatcher. Herein the mission in England, with Snake donning a coat, and with help from a mini mecha MKII. There's even hidden dialog with the lil guy (piloted by Otacon of course)
Zone of Enders - Vic Viper from Gradius (a classic Konami series) is a guest star character. Hidden at first, but is a playable character once found. Plus it retains some of its power ups, and the lazer shape shifts depending on the mode used.
This is just a few of the hidden easter eggs I know of, I will be sure to share more soon.