Have a ball or (better) a beanbag. Begin a story. Throw it to the person who must continue the story. This is better than dragging around the circle and shy people can get rid of the story after only one word.
A variation on this is “fortunately, unfortunately”. Each person must add a sentence, changing the sentence of the main character. E.g.
Unfortunately the plane’s engines failed.
Fortunately the pilot had a parachute.
Unfortunately the parachute would not open.
Fortunately their was a haystack underneath. Etc.