Extra credit is something I really want to do in my own classroom.
I know of one 6th grade teacher who creates packets of extra credit math each month. His students do them during indoor recess, on their own time, or when they are finished with their normal work. It's pretty cool. I walked in to observe his teaching on a rainy day and all his students were busily scratching away, solving math problems and logic puzzles independently as they took turns using the hall pass for bathrooms and drinks during recess. Best of all, they were focused and quieter than mice.
I used to give extra credit to students during exams. This never went very well - I don't like how it inflates grades to preposterous levels. I don't like how some students can fail the test, but get all the extra credit correct. Maybe the extra credit I gave was too easy.
What will my students get for doing extra credit? Hm, this bears some thinking. I probably won't use it to tack onto their grades. I'm thinking some sort of tangible prize, but I'm worried it might get expensive. Homework passes would be a good idea. Classroom privileges like more time on the computers may work too. That is, if I have computers in my classroom.