Narc was first a 1988 arcade game and was the first to be released by Williams after being acquired by Midway. Several ports were made to various home systems in 1990 including to the Commodore 64, Amiga, Atari ST, and NES. The home computer versions were all done by Ocean software while the NES port was done by Rare and published by Acclaim.
Most of the home ports were pretty average. I think the reason NARC is remembered today is because it was a controversial game at the time. It was one of the first games with this level of violence. The goal of the game is to arrest or kill various junkies, drug dealers and king pins culminating with Mr. Big. In the manual for the NES version of the game it was described as the first video game with a strong anti-drug message. Ironically, all references to drugs were removed from the NES version.
Nintendo has always had seemingly odd censorship rules. In this particular game, references to drugs were removed but most or all of the violence was retained. However, the splash of blood on the cover was changed to be yellow so it didn’t look like blood.
Midway Arcade Treasures 2 released in 2004 for the PlayStation 2, Xbox and GameCube had an emulated version of the arcade version of the game (with a few glitches) and in 2005 there was a remake of the game (also controversial) for the PS2, Xbox and PC.
The ad and screenshots above are all from the NES version.