The Legend of Zelda

This game is about a warrior named Link who has to rescue Zelda from Ganon. But to do so, he needs to reconstruct the Triforce of Wisdom in order to gain access to his lair.
This game was THE wide open game of the time. They just stick right in the middle of a vast land filled with forests and mountains and they just let you do whatever you wanted. You have very little clue on what to do from there unless you had played before or have a guide (cheat). There were many secrets in the game, from random people who awarded you money, to hearts that made you more powerful, to swords of legend, and the old man who makes you pay for the door repair. You could even complete the dungeons in any order you wanted (Well, to a point).
The game also had variety. While most games at the time gave your character one skill, Link acquired many different tools to help him. You have your wooden sword, bombs, boomerang, candle, ladder, raft, even a magic key that opens any door.
Those tools are necessary when you fight against foes that range from the feeble Octorock, to Like-likes, slime creatures that ate your shield! You also had the creatures that guard the pieces of the Triforce. Multi-headed dragons, Giant dinosaurs that ate ANYTHING, and even this... blob... thing... I still have no clue what the heck Dig-Dogger is.

Super Mario Brothers

Let's face it, almost everyone has heard of this game. Why not? It single handedly saved the video game industry from tanking into nothingness.
Everyone know its about a princess getting kidnapped, the hero has to save her, blah, blah, blah. Everyone heard that story... 50... no... 100 times now. But this game was messed up at the time. Flying Turtles anyone?
But this game dissappeared off of the shelves. Millions after millions of copies would be sold. Why? It was fun. It was the most advanced game at the time. There were different environments, varied sound effects, and many ways to fail. Horribly.
It was fun then, and it still is today, due to the many strange glitches in the game that shouldn't have existed. From the Minus World, to Small Fire Mario, this game had many glitches in it that kept it interesting. That's why people play it today.