For the last couple of years, my policy with regard to students' "extra credit" opportunities was entirely focused on incentivizing attendance for out-of-class lectures. If students attended a lecture and wrote a 2-page response essay, they could receive up to 5pts on their midterm or final exams. If they attended and asked a question, they could get the 5pts without writing the response essay. This was a really successful policy and I recommend it to others, especially those who (like me) find themselves frustrated by students' frequent non-participation in post-lecture Q&A sessions.
This semester, I'm trying out a new policy, inspired in part by an essay that I read many years ago in the NYT, "The Case for Memorizing Poetry" by Jim Holt. (I was reminded of Holt's essay after reading his excellent book Why Does The World Exist?: An Existentialist Detective Story this summer.) So, at the beginning of the term, I told students that there would be one-- and only one-- opportunity per month to earn extra credit in the course, but it would't be easy. It would require that they memorize a poem (selected by me), recite it aloud (with less than four errors), and explain to me what they think the whole (or some part) of it meant. I decided that I would select poems that were long enough to necessitate real commitment and a significant amount of time to memorize perfectly, in order to reinforce that "extra credit" is something for which one ought to have to do serious work.