Zed Fest says that they're seeking"low budget independent and amateur" films in the "zombie, horror, science fiction, and action genres."
It's interesting that they distinguish between zombie and horror films. Does this mean that zombies films are so prevalent that they're now a genre unto themselves? Certainly not every zombie film is horror. Many are comedies. (Usually, not too funny.)
Zed Fest also has a screenplay competition.
Their first screening was in 2010. They're based in North Hollywood and their 2012 screening is set for November 3, 2012.
For details on how to enter, go to Zedfest.org.
For a behind-the-scenes look at horror film festivals and the festival directors who manage them, see Horror Film Festivals and Awards. This book also includes a directory of over 200 horror film festivals, and a list of festival award winners from dozens of festivals over several decades.