Opinions and myths abound on this one! After looking at some trusted sites, the story seems to be that it's probably not a problem unless you plan on eating around ten pounds; but you'll probably want to cut out the green parts anyway. Here are three trusted sites -- the last one disagreeing with the first two.
Good Housekeeping ( http://www.goodhousekeeping.com/food/cooking/ask-susan-green-potatoes-1007 ) says it's not a big deal -- you'd never eat enough to worry about.
Kansas State University ( http://www.k-state.edu/media/WEB/News/NewsReleases/greenpotatoes101404.html ) The plant pathologist interviewed never saw a person develope a reaction -- you would get a bellyache before ra reaction. Besides, you can simply cut the green part out anyway.
Cooperative Extension ( http://www.extension.org/faq/4200 ) This one recommends " To be safe, it is best to not eat green potatoes."
Potatoes naturally contain some amount of the toxin solanine and are members of the nightshade family. When exposed to sunlight, potatoes turn green under the skin and the levels of solanine are increased.
Most health professionals recommend that any potatoes which have turned green be thrown away. It is probably safe if you just remove the green bits and the eyes or sprouts as they also contain high levels of solanine.
Reactions to ingestion to solanine can range from mild nausea to convulsive vomiting and diarrhea. High levels cause more severe and life-threatening reactions.
See my answer to: Are potatoes poisonous?
A better site to check is NIH's Medline.