In general, I'm not a fan of extra credit. Students, of course, love it. For them, it's a kind of second chance. The problem is, they also tend to think of it as "free" points. They don't view it as a second chance to learn something; or an opportunity to learn content beyond the course syllabus. Rather, in my experience, they often treat it as something they will sort of take a stab at and then expect to get the maximum number of offered points. Over the years, I've started offering some extra credit on exams and also to final grades in large enrollment classes. Partly, it's my way of making up for a question on the exam that may have been unexpectedly difficult for most students; and it's a way of telling them that I won't negotiate on final grades. It gives them the chance to cover those small gaps between letter grades and leaves me giving them whatever grade they earned without feeling bad for the student.
This semester, I have been amazed to observe the way my students behave at the first mention of extra credit. They remind me of my kitten, a food hound, who runs as fast as he can to his food bowl when he hears me pouring in his kibble. Part of what amazes me is the fact that these are the same students who, as a group, won't follow any of my advice about how to prepare for exams. I can tell them that preparing for class regularly, attending class, and participating in the class activities will raise their grade, on average, 10 points and they don't want to hear it. But they will expend a tremendous amount of effort for two points that are guaranteed. Among other things, my observations have reassured me that the way to approach this group is to reallocate all those midterm points to quizzes, homeworks, and other "small stakes" assessments. They have to see the immediate payoff (woot, I got 2 points for doing my homework today) in order to behave rationally. If I simply tell them that doing their homework daily five classes in a row will add ten points to their grade, they wouldn't do it.
This seems to be a generation whose pleasure and reward circuit is wired entirely different from my own. I find it difficult to relate to an audience of students who require constant, tangible incentives to behave rationally. At the same time, it's my hope that, in a way, I can train them in how to do this and then, as they progress through college, they will not require quite so many immediate rewards (though half of my students are already upper division students). I also suspect that I am encountering a large number of students from the sciences who are accustomed to daily homework sets. They have never been taught how to learn in a humanities class and, for various reasons, aren't inclined to listen to the advice of the instructor.