What are your thoughts on extra credit? What is EXTRA CREDIT? If you do give extra credit, how do you determine what is EXTRA CREDIT and how do you grade it? How does it influence a student's grade?

Looking forward to your thoughts.

GL-
Extra Credit is arguably an extremely debatable topic in the world of education. Whereas some teachers believe that credit earned is credit due, others believe that extra credit puts students in a position to be irresponsible and over time make up for lost or missing work.
In High School, it was always very difficult to hear a teacher deny me extra credit when I worked hard in class, but just wasn't quite earning the grade I needed. I often heard the response "I don't offer extra credit because I have to offer it to all students." I tended to always think that was ridiculous considering everyone else had the opportunity to ask for extra credit. That always seemed to see the most common response, that or simply just "I don't offer extra credit."
Now that I am in a classroom regularly it is easy to see the reasons why this is true. Imagine this scenario. Student A is struggling in class. She is always prepared for class, participates regularly (be it that her responses in class are often incorrect), sits quietly during class, and has no late assignments for the semester. Student B has the same grade as student A. However, she is rarely prepared for class, interrupts class, is often rude to her teacher, and has several late or missing assignments. At the end of the semester, both students express that they need extra credit to attempt to boost their grade. The ultimate question is who is more deserving?
After doing reading several articles online, there is one theory I hop to adopt when I have a classroom of my own. It generally revolves around the scenario involving student A. Some teachers have adapted the "if you are willing to go the extra mile" approach. This approach essentially takes the idea that students who have made a genuine effort earn the grade they currently have can take the opportunity to work the extra mile to earn a few more points. This approach prevents students who have chosen to slack off all semester from trying to earn points just because they need the grade, not because they have earned it. For this approach though, it is important to set the guidelines from Day 1 so that when the time comes for students to beg for more points, you have an objective defined line that shows whether or not the student has earned that right.

Here are several other links that you may find useful:
http://712educators.about.com/od/gradingsystems/a/extra_credit.htm
http://voices.washingtonpost.com/class-struggle/2009/05/extra_credit_do_schools_push_h.html
http://www.city-data.com/forum/education/1184626-how-do-you-feel-about-extra.html