On all the biology-related question/answer sites I've seen, one of the most common questions is a variant of the eugenics-tinged "Has medicine/society stopped human natural selection?" The most recent version is Has human evolution currently stopped?; previous versions include Has medical progress stopped human evolution?, closed as a duplicate of Is better healthcare a bane to the long-term survival of the human race?.
The answers to the "original" are decent, but not excellent; there are multiple publications (peer-reviewed and otherwise) that directly address the question that could be cited.
Because the question is so common, because it draws poor-quality answers, and because there are multiple references that could be used to answer it, it seems to me that this would be a good case for a Community Wiki type answer, folding in the present answers with added references. The question could also be slightly broadened for clarity, e.g. to cover claims other than health care (I voted to close the most recent version as a duplicate, but the poster claims it's not a duplicate because his trivial variant makes it a completely different question).