You have got some great advice from the previous responders. Let me point out a few places where people really go wrong in their story telling - avoid these mistakes:
1. A lot of people who use quotes tend to forget that it should also have a relevance to their story. The quote begins to stand apart and the reader is left wondering why it was there in the first place.
2. Many applicants are unable to weave a common thread through their essays, especially in the behavioral ones. They tend to start the essay from point A (introducing one of their strengths), explain it through an anecdote, and conclude at point Z (introduce another strength, rather than concluding the first one). Closing the loop is important.
3. In the anecdote itself, its your role in that situation which is most important, not the situation itself. A lot of applicants spend all their space situation building and the reader gets no idea about their problem solving skills .
4. Maturity- this should reflect both in the way you handle the situation, as well as write the essay.
Hope these help,