Megaman

This one is definitely one of my favorite games for the NES. You play as an advanced robot from the year 200X (I haven't seen him yet.) whose job is to take down 6 others that are wrecking havoc on the world.
This game was unique at the time because you could select the stages you visit in any order you wish. This gave the game a sense of being open and the feeling of doing what you want. But, there are better ways to go through them than others.
You see, this game's true power shines through the powerup system. You get to the robot master at the end, you beat him down in an all-out brawl, and you got his weapon. Now you can do what they could do, and their power ranged from scissors that acted like a boomerang, to a three-way electricity wave that fried everything above, below, and in front of you. The most important use of these weapons, however, was exploiting the weaknesses of the robot masters. Each of them was vulnerable to another one's weapon, and once you figured that out, it was clobbering time.
But the game was HARD. This game was pretty difficult normally, due to some nasty enemies, but it had some nasty demons in there: Iceman's shooting platforms of doom will shoot you down if his appearing and dissapearing platforms didn't and Elecman will fry you in three shots AT MOST. But Gutsman's mining platforms and the Yellow Devil will forever remain hated in the hearts of gamers everywhere.
If you are ready for a challenge, go ahead and try it. But don't say I didn't warn you.

Metroid

You are Samus. Your mission is to infiltrate Zebes and defeat the Mother Brain. Simple, right? Not really.
Metroid introduced a new kind of gaming into the world. You would have to navigate an alien world fighting off all sorts of deadly foes, trying to find the Mother Brain's lair and destroy her. This is MUCH easier said than done. The creatures ranged from the spiked Zoomers that crawled along the walls, to the deadly Metroid that chased you down and sucked your health down.
But the biggest reason it was difficult was its maze-like nature. You will be lost. You will running back and forth between rooms you have been, your health most likely being sapped by the enemies and the environment. You will be blowing up random spots in the walls and floor in the vain hope of finding a way to progress somewhere else. You will find a secret passage, only for it to lead into a dead end.
Don't worry, you can find enhancements to help you out. Missles, bombs, the Ice beam, and even the ability to curl up into a ball will help you navigate this maze... IF you can find them of course.

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.