The Addams Family is a licensed platformer created by Ocean for the SNES, Amiga, Atari ST in 1992. It was ported to Sega Genesis in 1993. Ocean also made similar versions of the game for 8-bit platforms, like Commodore 64, Game Boy, ZX Spectrum, Sega Master System.
In the game, inspired by the movie of the same name released in 1991, you are Gomez, and you have to save the rest of the family: Morticia, Pugsley, Wednesday, Granny, and Uncle Fester. There is no shooting; this is a pure platformer, with a mechanic, in part, inspired by Super Mario. In fact, you have to kill enemies with a jump on their heads. But the gameplay is nonlinear and could also be defined as "Metroidvania." Gomez can explore the house freely without needing to follow a specific order. There are also plenty of secret passages and side levels. A door that was leading to the room may lead to another place the next time you open it, which makes the task of visiting this vast mansion very hard.
Overall, Ocean did an excellent job with this game: the controls are responsive, the animations and scrolling are smooth, the soundtrack is perfect. The graphics are also superb (but better on Genesis than Amiga, since the Amiga version is missing the background).
All the reviews of the magazines were highly favorable and for a reason: this is one of the best movie-inspired platformers ever created. Whether you are a fan of the Addams family or not, this is a game you have to try.