Here are two stories that come from authors who have since become household names in the zombie genre:
Neil Gaiman's "Bitter Grounds"
"Bitter Grounds," a free zombie story by Neil Gaiman, was reprinted on the Tor site at the beginning of zombie week. "Bitter Grounds" first appeared in 2003, in the book Mojo:Conjure Stories. The same zombie story came out later in Gaiman's collection called Fragile Things. Tor published the story in its entirety as part of Zombie Week on September 13, 2010.
From "Bitter Grounds"
In every way that counted, I was dead. Inside somewhere maybe I was screaming and weeping and howling like an animal, but that was another person deep inside, another person who had no access to the face and lips and mouth and head, so on the surface I just shrugged and smiled and kept moving.
David Wellington's "Good People"
"Good People," is a zombie story by David Wellington that first appeared in the anthology The Living Dead 2. David Wellington is the author of the free zombie fiction book Plague Zone. Wellington's website has links to much of his other zombie fiction.
From "Good People"
The dead man was only a couple feet away from Candy when I saw him. He was on the wrong side of the chain-link fence but he was leaning on it, hard, and it was starting to sway. His clothes were bleached white by the sun and his skin was gray. His lips had rotted away, like most of his face, and his teeth were huge and yellow and broken until they looked very sharp.
Candy was three years old. She didn’t even look up.