Milgram was unethical due to the severe emotional distress of many of the participants, and it was part of the impetus for the development of the modern Institutional Review Board structure and Informed Consent requirements for psychological experiments.

Its findings are somewhat less suspect than Zimbardo's in the Stanford Prison Experiment (which is now fairly widely panned as a godawful experimental design and implementation, even apart from its ethical problems), but it's still seen as a very big signpost saying What Not To Do.