It should be something someone reading your resume nods at but doesn't challenge you about in the interview. A lot of people continue to view education as: "if there is no qualification it didn't happen." So you'll find people (particularly older people) asking you what qualification you got then outright discounting the entire thing if you got none.
If there's a manager that knows about MOOCs, they'll notice.
If there's a manager that doesn't know about MOOCs, they'll either gratefully receive a new thing to try, or will not care.
I don't see a downside.
It indicates to employers that you have an inherent drive to learn things (i.e. beyond what is required as part of your formal education). And that is a good thing.
It depends on which country you're in and where you're applying.
US-style resumés are VERY different from, say, European-style Curriculum Vitaes (also used in 3rd world countries like mine).
In a CV, I would definitely add them. In an US-style resumé, I'm not so sure how they fit (seems like UnoriginalGuy has some good advice)