The First Line is a literary magazine whose quarterly issue is always based on a sort of writing competition. The magazine offers the first line of a short story (hence its name), and writers develop the story from there. It is fun watching how the stories all turn out so differently, but from the same starting point.
At my main blog site, it is a common practice for us to initiate various writing challenges. I've started one here based on the idea of The First Line. The links to the stories that have come out of that challenge can be found in the comments section there.