The Addams Family is a side-scrolling action-adventure platform game. The story involves Abigail Craven scheming to obtain The Addams Family's secret wealth. To do this, she brainwashes Uncle Fester, who has just lost his memory, into being an ally. She is also aided by The Judge and the Addams' family attorney, Tully Alford, who takes control of the mansion. Morticia Addams, Pugsley Addams, Wednesday Addams, and Granny go to the house to meet with Tully about the property, only to be kidnapped by Abigail. When Gomez Addams arrives home, he discovers that the other family members are missing. To save his family, Gomez runs, jumps, and squats his way throughout the large mansion infested with ghosts, mutants, monsters, bats and rabbits, as well as stage hazards like stars, swinging clock pendulums, and fire lakes.
Puzzle-solving is also involved in saving the Addams family members. For example, Wednesday is found in an ice-themed freezing area and it is up to the player to figure out how to free her. Granny is also trapped in a stove which is turned off by a switch that the player must find. The Amstrad CPC game has many doors that can only be unlocked by keys hidden throughout the mansion. In most versions, the underground chambers must be activated to save Morticia; Lurch plays a tune in the Music Room that activates it, but only when Wednesday, Pugsley, Granny and Uncle Fester are rescued and meet up in the room. In the NES version, Gomez has to collect $1,000,000 to save Morticia. The Judge is the final boss.
The Addams Family is similar to open-ended titles such as The Legend of Zelda and Metroid (both 1986), as the player has the freedom to navigate both the indoor and outdoor areas of the mansion in any order. The core of the game is in the mansion's Hall of Stairs, consisting of the front entrance and six doorways. The rooms these doors lead to include the kitchen, the games room, and the portrait gallery, and each feature around 40–50 screens. A huge bird is located in the outside garden and serves as a boss. One of the doors near the front is invisible and leads to Pugsley's Den, which has power-ups, money, and five 1-UPs. It also has another secret area containing 27 lives. Throughout the mansion, there are certain areas holding extra lives and money, as well as unnoticeable spots in non-secret locations with the same sort of bonuses. There are also boxes where Thing provides clues, such as how objects in a room work and which place to go next.
Similar to Mario games, Gomez kills enemies and bosses by stomping on them, and collects power-ups and coins. Power-ups include a sword, a golf club that can shoot balls, the fezi-copter hat that makes Gomez fly, and shoes that increases his speed. All of these can be held from door-to-door except for the fezi-copter, which disintegrates by the time Gomez enters a door. The version additionally has four collectible potions, left around by Pugsley, that are needed to access certain areas. The Wolfman potion increases his speed, Frankie gives him invincibility that lasts for 10 hits with enemies, Sea Monster enables him to swim underwater, and Drac makes him fly. In the Game Boy release, power-up items are limited in energy, meaning power vials must be collected to keep them in use.