A source for information about free contests can be found on the blog Publishing . . . And Other Forms of Insanity. Lots of flash fiction contests are in the list right now, for those who have recently discovered an interest in very short stories.
The same blog also includes information about publishers who accept unagented manuscripts without fees and Calls for Submissions including poetry, short stories, essays, and creative fiction and nonfiction.
Thanks go to Muriel Sandy for suggesting this resource.