Zombies have completely permeated the American culture. There are books, graphic novels, TV shows, and movies of all sub-genres (comedy, drama, thriller, and horror) based on the zombie apocalypse. But where did they come from?
Countless cultures, religions, and folktales involve the living dead. One of the most well known pagan cultures that focus on the living dead are the Vikings: In their foretold tale of the war that will destroy the world, Ragnarok, Loki will bring an army of dead men from Niflheim (the land of the dead) and the Norse gods will bring their army of the dead from Valhalla (the hall of fallen heroes - men who died in combat) to fight each other until the world crumbles.
Also, in one of the most well known literature books, Dante's Inferno, there are 9 circles of Hell, each dedicated to a different punishment for a different sin; and in the 5th circle, dead men and women fight each other, punching, kicking, and biting each other forever as retribution for letting their anger control them in life.
Furthermore, stories of the undead that feast upon the living are very common in ancient myths and folklore, vampires and banshees being a couple of the most well known. There are also accounts of people once thought dead who rose from their grave, still breathing; and ghoulish activity. (The word "ghoul" means a person who eats the dead.)
Undoubtedly, the evolution of what has become the modern conception of a zombie has been influenced by many different things. However, there is one culture that has the strongest connection to what we consider as a modern-day zombie - the culture that created the word zombie: Voodoo.
Voodoo is a syncretic religion of Roman Catholicism and traditional Haitian culture. Voodoo says there is one creator (God) and the spirit world where He, and all of the dead, reside; and it is most well known for its practices in magic and making human connections to the spirit world via possession by spirits.
In the Voodoo tradition, there are sorcerers who abuse their magical powers to possess other living people. These sorcerers are called bokors, and they supposedly steal the souls of other people, turning them into mindless slaves with no independent will. This kind of slave is called a zombi.
The way the bokors perform their "zombification" is with zombie powder. Zombie powder is scientifically called tetradotoxin, and it is a powerful nuerotoxin that induces a coma and slows the breath and heart rate until they are nearly undetectable. When the person comes out of his or her coma, which they inevitably will, the bokor then forces them to take "hallucinogenic compounds... put[ing] the victim into a permanent state of delirium and disorientation in which they experience delusions and hallucinations." In this state they can be easily manipulated into doing labor.