Of course, zombies and Crazies go back much further than the Cold War, and some might even tell you that they have basis in fact, so let's start with a little zombie refresher course before we get to the heights of zombie-mania in fiction and film. Many people will tell you that zombies and reanimation of dead tissue extends back to the origins of Voodoo and Afro-Caribbean beliefs. The story goes that the "Ti Bon Ange" (or the soul) can be stolen from a body, creating a lifeless, brain-dead slave. At first, in most pop culture, that's all that zombies were, but horror and supernatural fiction slowly evolved the concept into something far more sinister. Suddenly, zombies weren't just brain-dead slaves, they were brain-hungry villains. There have been alleged "true stories" of zombies throughout history, including the adventures of Wade Davis, a doctor made famous in The Serpent and the Rainbow for investigating zombie practices in Haiti in the early '80s, but there are also "true stories" of vampires and Bigfoot, so it really all comes down to what you're willing to label as "true."
In American pop culture, zombies go back to the days of H.P. Lovecraft, who wrote stories about the totally insane Dr. Herbert West, made popular in present day by the Stuart Gordon movie, Re-Animator. In Lovecraft's fiction, West would try to revive human tissue with zombie-like results. Even earlier than that, there are references to brain-dead men walking the earth as early as 1697, in a French novel called The Zombie of the Great Peru. In a French dictionary a hundred years later, the word would be used again in reference to Haiti, mentioning that floods in the area would sometimes bring buried bodies back to the surface, probably influencing the idea that the dead were returning to life.
The first landmark in the modern history of zombies in pop culture came in 1954 with the publication of I Am Legend by Richard Matheson. Legend is about a lone man in a post-apocalyptic Los Angeles that has been overrun by bloodsucking ghouls. They're not your traditional or even your modern zombies, but Legend had a huge influence on the way zombie culture would transform over the next half-century for two main reasons. First, Legend inspired the President of Zombie-dom, George A. Romero, to make the most famous zombie film of all time, Night of the Living Dead, and second, it set up a structure that would be copied by zombie movies from then on -- a small group of people, sometime only one man, trapped in one place, surrounded by a sea of the undead. I Am Legend solidified the theme of "the evil of the world outside the home" that zombie movies would make their own for the next five decades and counting.