I've done this with almost every level of student that I have taught. It's similar to the game telephone, in which you start a story and pass it along, although this story is written down. I write a story starter the first time we do the activity on the top of a piece of paper, one for each student in the class. (Or you can write one for a center activity and leave it there throughout the week). Each student writes a sentence or paragraph and passes the story along, until everyone has added to it. Then the stories are shared aloud at the end. This works really well with upper elementary and high school level students. I use it a lot with ESL students and reading aloud at the end is fun for everyone and helps them work on pronunciation. Kids are also not shy about sharing because the writing belongs to the group and is not solely theirs.
After you have done the activity once or twice, the kids like to start the stories themselves.
This activity can take a lot of time, if you are passing the writing around the whole class. To shorten the amount of time, you can limit it to small groups, chart paper in which kids add when they have time, or as mentioned above, leave it at a center.