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.