Ghostbusters was published by Sega and developed by Compile for the Mega Drive/Genesis on June 29, 1990. It is unrelated to the earlier Activision game (though their name still appears in the copyright screen), and is instead a run and gun game in which the player takes control of squat cartoon representations of three of the four Ghostbusters from the movie, with the noticeable absence of Winston Zeddemore. Four levels are available initially; after they are completed, a fifth level is unlocked, followed by a sixth and final level. Each level contains a number (usually two) of mid-bosses known as "middle ghosts"; after a middle ghost is defeated, it turns into a small green ghost which can be captured for extra money by luring it over a ghost trap. Between levels, money can be used to buy powerups, such as a 3-way shot or recovery items.
The Ghostbusters are down on their luck due to lack of ghost activity, when suddenly several calls begin to pour in from around the city, including the eventual reappearance of the Stay Puft Marshmallow Man (although dialogue indicates it is not the same one from the movie). After each case, a piece of a stone tablet is collected. The three Ghostbusters piece together the mysterious tablet, inadvertently opening a portal to "the evil world" and releasing a horde of ghosts. In the end, though, the Ghostbusters manage to defeat Janna, the God of Darkness, and retrieve a mystical gem from the evil world. They combine the gem with the tablet to close the portal, and save the city.
Source: Wikipedia, "List of Ghostbusters video games", available under the CC-BY-SA License.