Hi Carol:
I think adding bonus questions or essay type questions are good learning tools. I know some teachers like to drop the lowest quiz, especially when there are 12-15 quizzes in a session. For me, these are related to learning and although they "monkey with the grade a little, it's based on student learning (or lack of).
By contrast, extra credit that is given in place of low assignment grades due to missed or late assignments, or worse, in substitution for regular assignments - that's just unfair. Good students who work hard may take offense; some may percieve EC as unfair; it's subjective to grade; and arbitrary if some students get the opportnity and others don't.
Long ago, I learned my lesson, and decided I just don't give EC. I work in a healt setting where literally, life and death decisons are made by these workers (Respiratory Therapists). There can be no room for error. So I just don't give it. My opinion for my classes. Each institution and teacher has to decide what's best for their classes.
Regards, Barry