The arcade version of Ninja Gaiden (released in 1988 in North America and Europe, and 1989 in Japan) was a Double Dragon-style beat 'em up, in which the player controls a nameless blue ninja as he travels to various regions of the United States (such as San Francisco, New Jersey and Las Vegas) to defeat an evil cult led by a fictional descendant of Nostradamus, who is trying to personally fulfill his ancestor's prophecy of the rise of an evil king in 1999. The player has a variety of techniques, such as a flying neck throw and a back-flip. The player can obtain power-ups by throwing enemies into background objects, such as street lights and dumpsters. The player fights primarily with his bare hands, although a sword can also be used for a limited time as a power-up; he can also use environmental objects as a prop from which he can deliver more powerful kicking attacks. Although the game takes place in different environments, there are primarily only five kinds of enemies, all of which appear in every level (although some levels have extra enemy types). The game is mostly remembered for its infamous continue screen (where the player character is tied to the ground underneath a descending circular saw).
While the game itself bears little or no connection to the later NES trilogy or Xbox revival (although the Xbox version does feature the same flying neck throw from the arcade game), certain aspects of it were carried over to the first NES title. The first stage in the NES game is a loose adaptation of the first stage in the arcade game and the opening cutscene in the NES game vaguely resembles the intro in the arcade version. Both games also feature Jason Voorhees look-alikes and the final boss in the arcade game vaguely resembles Bloody Malth from the NES game.
Source: Wikipedia, "Ninja Gaiden", available under the CC-BY-SA License.