The BBC National Short Story Award competition is now in its fourth year. It's not genre, but neither does it exclude genre stories. The competition is only open to writers who "previously have had works of prose fiction, drama or poetry published by a UK publisher (excluding self-publishing) or established printed magazine in the UK or broadcast by a UK national radio station".
Word limit is 8,000 words. Deadline is 5 p.m., 15 June 2009.
First prize is £15,000. Runner-up gets £3,000, and three other shortlisted stories wil lreceive £500 each.
See here or here for more details, entry form and terms and conditions (note: both are Word documents).