Kid Icarus (NES, 1986)

The Greek myth of Icarus tells the story of a man and his father, who fashion wings out of wax and feathers in order to fly and escape from prison, but Icarus does not heed the warnings of his father not to fly too close to the sun, and his wings melt, dooming him to perish in the sea.  Kid Icarus (1986) is not a video game retelling of this story, but does use Greek myths and legends as its base.  It is also an amalgam of every style of gameplay that was available on the NES, from platformers to shooters to dungeon crawlers and RPGs, and a nearly flawless mixture of all its elements.
In Kid Icarus, you play as the angel Pit, a tenderfoot soldier in the goddess Palutena's army.  One day, the ruler of the underworld, Medusa (not Hades) invades Angel Land, imprisons Palutena, and turns all of her soldiers to stone, except for Pit.  It is up to Pit to rescue Angel Land.  Having been cast out by the attack, Pit must climb from the underworld, to the Earth, scale the clouds and return to the overrun Angel Land Kingdom.  To help defeat Medusa, Pit must also collect three sacred items (the legendary bow, wings, and shield).
Kid Icarus has been described as a mixture of Super Mario, Metroid, and The Legend of Zelda, and that is pretty accurate.  Like Super Mario, each level is designed with an emphasis on platforming.  Like Metroid, you fight by shooting at enemies and gain power-ups.  Like Zelda, every four stages there is a dungeon  with a boss to fight at the end.  Killing enemies grants you points, and every ten thousand points your health bar is increased.  All of these very different elements come together seamlessly, and make a game where every new level is a fresh and new experience.  Everything is held together by the game's marvelous aesthetic, which for the first time on the NES, was starting to look realistic.
This is not a perfect game by any means.  It has its share of flaws which can make it frustrating at times.  The controls can be a little slippery, which is made obvious by the fact that many levels require you to jump with precision across skinny platforms.  The difficulty curve in this game is all over the place.  The beginning of the game offers the most challenge since you are at your weakest, and then levels off at an easier pace once you start getting more powerful.  Some of the enemies in this game can be downright sadistic, such as the grim reapers, who will send a plague of mini-reapers after you if it spots you.  There are the infamous eggplant wizards, who will turn you into a helpless eggplant, and the only way to change back is to find a hospital hidden away somewhere in a dungeon.
The game's shortcomings are overshadowed by its many great traits.  Since no two levels are the same, there is a high incentive to keep playing to see what challenge lay before you.  This is one of the first games to offer multiple endings based on how well you do in the game, which gives it a good amount of replay value.  Then there is the feeling of satisfaction you get for completing each level.  While the game is frustrating at times, I can never call it unfair.  If you die, you are sent back to the beginning of a level, but you are given infinite lives, and a password each time you die (which you can use to resume playing if you leave the game).  This is one of the most difficult games on the NES, and completing the game is one of the most satisfying feelings you can achieve as a gamer, and the ending is rewarding enough to make it worth your while.
Kid Icarus was not a huge success upon first release.  It gained something of a cult following in the years after its initial run.  There was a sequel on the Game Boy, called "Of Myths and Monsters," but Pit would not make another appearance in a game until he was made a playable character in the fighting game Super Smash Bros. Brawl, approximately fifteen years later.  He recently got another game of his own on the 3DS, Kid Icarus: Uprising.  The NES game will always be a gem of its illustrious library, and one of Nintendo's finest and most criminally overlooked achievements.