The list today are sites that have various challenges and or contests.
Membership - Free http://showmeyourlits.com Show Me Your Lits is a membership site that holds weekly flash challenges. You sign up to become a member and on Sunday the prompts are posted and you have ninety minutes to write a flash story before Tuesday. The stories are posted on Wednesday for comments and voting. The people are friendly and a literary sort.
Membership - Free http://libertyhallwriters.org A sister site for those who prefer the spec fic, fantasy, sci fi, horror genres. Again, a great group of writers who give excellent feedback on flash drafts. They hold weekly flash challenges though it works a bit differently and they start their flash week on Friday. They also hold short story contests occasionally and polish challenges for those wishing to polish up stories for submissions.
Toasted Cheese Literary Journal - http://tclj.toasted-cheese.com/
A great literary journal with forums and quarterly contests.