This is the series for the two consecutive Addmas Family games, for all the others use only the franchise.
Six video games released from 1989 to 1994 were based on The Addams Family. Fester's Quest (1989) was a top-down shooter that featured Uncle Fester saving the World from an alien invasion.
Two versions of The Addams Family were released by Ocean Software based on the 1991 Movie; an 8-Bit version for the Nintendo Entertainment System, Game Boy, Sega Master System, Sega Game Gear, ZX Spectrum and Commodore 64, as well as a 16-Bit version released for the Super Nintendo Entertainment System, Amiga, Atari ST and Sega Mega Drive/Genesis.
ICOM Simulations also developed a game based on the movie for the TurboGrafx-CD.
The games' sequel, The Addams Family: Pugsley's Scavenger Hunt (1993), also by Ocean Software was based on the ABC animated series and was released for Super NES, NES and Game Boy (although the latter two were just 8-bit remakes of the first SNES game, swapping Pugsley and Gomez's roles).
Addams Family Values (1994) by Ocean was based on the movie's sequel and returned to the style of gameplay seen in Fester's Quest.
A Game Boy Color game was released in the 1990s for promotion of "The New Addams Family". The game was simply titled "The New Addams Family Series". In this game, the Addams mansion had been bought by a fictional company called "Funnyday" that wanted to tear down the house and surrounding grounds to make room for an amusement park."
Source: Wikipedia, "The_Addams_Family", available under the CC-BY-SA License.