Kathryn,
I have used essay style question(s) in an exam as a way to offer "bonus" points and perhaps measure the students learning a bit more accurately. For these questions, the bonus points represent a very small percentage of the total exam score. As a rule, I do not give extra credit to the degree that it would affect a students grade. I want to measure learning, not be in the point-giving business. However, I do let students do extra work (non-assigned workbook, project, papers, etc.) with the student knowing in advance no extra points will be given. In these instance, my reward to them is praise and recognition to them and their class, something often more valuable than points.
Barry Westling