It's not hard to see why they didn't really catch on, but they did figure in some films, with "White Zombie," starring Bela Lugosi, and Val Lewton's "I Walked with a Zombie" among the best-known and most highly regarded.
Then "Night of the Living Dead" came out, and our view of zombies changed forever. Originally titled something like "Night of the Flesh Eaters," the film never refers to them as zombies, and the film's director George Romero said he considered them ghouls, another mythological supernatural creature, albeit one that is born that way and eats not the living but the already-dead in cemeteries. "Living Dead" itself is a generic term for several supernatural creatures, usually vampires. The idea that the victim of a zombie becomes one too is clearly a variation on the vampire and werewolf legends. In voodoo, the zombie is created by a houngan, a kind of witch doctor or priest.
After NotLD, numerous other flesh-eating "zombie" movies followed, many in Italian cinema. Romero did a couple of sequels, notably the slightly satiric "Dawn of the Dead," then humorous films with zombies started popping up ("Return of the Living Dead" and "Shaun of the Dead" among them). Variations like "28 Days Later" appeared, although again these weren't zombies but living people infected with a so-called "rage virus." They moved fast, and soon "fast zombies" were running amok, including in an irony-free remake of "Dawn of the Dead." Even non-zombie stories such as "I Am Legend" (a vampire story originally) were re-imagined as "zombie" films.
Some of the "truest" fictional zombies were assembled in Marvel Comic's "Tales of the Zombie," while new school zombies mix with ~ and eat ~ their super hero characters in the "Marvel Zombies" series.
Zombies of any type still didn't fill a lot of books though until Max Brooks wrote and published the humorous "Zombie Survival Guide" and "World War Z," an "oral history" of the "zombie wars." Then someone came up with the idea of taking a public domain book and adding supernatural creatures, starting with "Pride and Prejudice and Zombies" and including "The Adventures of Huckleberry Finn and Zombie Jim."Now zombies or zombie/flesh-eater hybrids are all over the book store shelves too.
If you're looking for some zombie lit, be sure to visit to the horror section of your local bookstore, or search your favorite online store. I've got one on my reading list: "Handling the Undead" by John Ajvide Lindqvist (author of "Let the Right One In/Let me In," upon which the recent films were based). "Hater" by David Moody looks worth a look too.