Add a 'delete' button to the contest edit page. Only admins can delete contests, and they'll have to confirm that they want to (after pressing the button).

I don't think there's that much to worry about with deleting, because there's not really any crucial data to a contest. (Hm, although maybe once we've added the 'select winners' feature, we'll want to be able to export a contest summary to wikitext prior to deletion?).