Role-Playing Games
Zombies are one of the most recognizable creatures in role-playing games like Dungeons and Dragons, and many times players lay out entire campaigns regarding zombies. However, some games, like the infamous All Flesh Must be Eaten, are about nothing but zombies, and a world in which the living dead are a plague among the survivors of the living. If you have a group of friends and a storyteller, one of these games can last for a large number of sessions.
Card and Board Games
Zombies have always been a part of collectible card games that include fantasy settings like Magic: The Gathering. However, some games on the market have zombies as a central feature of play, such as the card game Give Me The Brain. The combination card and board game Zombies actually puts players in the center of a town that's been overrun by the living dead, and it's every man for himself as all players try to escape.
Video and Computer Games
Zombies have been the subject of video games ever since the infamous grandfather of first-person shooters, "Doom," used them as baddies. Moving on to create the "Resident Evil" franchise, and putting in appearances in "Half Life" and other games, zombies are a huge part of video games. Additionally, there are Flash games you can play on the computer for free like "Outbreak," where you orchestrate a zombie plague and take over the world. You can play games like this for free as long as you have an Internet connection.
Live Action Games
While not always games, there are certainly no shortages of events that involve zombies. Zombie marches, where huge groups of people get together in zombie clothes and makeup and wander through a city like a parade of the living dead, are always a spectacle. You could also add a twist to games like tag by making the person who is "It" a zombie; alternatively, you can make that person the only human and everyone else zombies out to eat that person.