Ninja Gaiden was first introduced as an arcade game in 1988, but with a different plot. In the NES version, the story follows Ryu Hayabusa on his journey to America to avenge the murder of his father. Along the way, he is recruited by the CIA to prevent a villain known as the Jaquio from merging two demon statues and taking over the world.
While the plot sounds like one from a schlocky B-movie, it was one of the first games to feature a story with twists and turns. Its 20 levels are divided over 6 acts and reaching the end is difficult. Not that this is a testament to its toughness, but I have never beaten the game in my 20 years of playing it off and on.
The success of the Ninja Gaiden spawned two sequels, and versions for Sega and Xbox have since been released. IGN lists the original Ninja Gaiden as the 17th Greatest NES Game of all time.