Can I include in my academic CV that I have attended and completed the Coursera and Udacity classes I have been taking? I understand that these are not anything major, but the courses definitely gives a good overview and starting formal study on the subject becomes less cryptic. If I can include them without any negative impacts, then under what section should I include them?
If the online course is relevant to your current field of work/study it would help. For example, a graduate student of science could mention a course on scientific computing but a course taken on criminal law would be irrelevant. Also online courses taken can only be shown under professional development and not under academic qualifications since these are non-credit courses.
Yes. The certified courses that connect to skills that doesn't directly apply to your mainstream degree deserves to be in your academic CV. It will show, to an extent, an interdisciplinary qualification that you possess. There are many real life instances where this has helped a lot, especially in industrial placements, career change, and interdisciplinary research.
There are some courses from MOOC you ought not to add in your CV. These include those that overlaps the courses you've already completed as per your educational degrees, minor introductory courses, and those that wouldn't prove a significant impact in your career point of view.
Interesting to see how things have changed since 2012 when I asked this question. I started with some artificial intelligence and machine learning coursework in my masters, and afterward attended the first machine learning and probabilistic graphical model courses, which started Coursers (the first ones before Coursera was founded).
Although I did not need to list these courses in my CV, I think if it is certified, it is definitely worth having it in the CV depending on what position one is targeting to apply for. For example, if someone wants to apply for a position where statistical analysis and modeling skills with R are needed, then it is worth listing relevant courses (preferred certified) in the CV. I believe that it will show that the candidate has some skills with R and statistical analysis. It is good to have this is a CV for the industry that may add real value.
Although for an academic CV, I somewhat agree with @JeffE . It may be good to have this in an undergraduate or master's CV if the course is certified, and you want to showcase that specific knowledge that probably is not covered in the curriculum and you want to highlight it. Afterward, when things become more specific, these definitely become pointless.