There have been many experiements over the years concerning people's obedience.
The most well known one was conducted by Stanley Milgram in 1961 where he got a number of individuals to willingly administer electric shocks to an individual who got set questions wrong. Each time they got a question wrong, the level of electric shock increased. What the individuals didn't know was that the "victim" was in on the experiment, wasn't getting shocked at all and was deliberately getting the questions wrong to see if they would still shock them despite the shocks reaching deadly levels.
It turned out that 65% of the individuals obeyed the experimenter and administered the highest voltage of 450 volts but 35% refused to go this high. Of course, those that did administer the highest voltage suffered from negative reactions such as sweats, groans of regret, digging their fingernails into their hands and sighing from relief that it was over. Some even had seizures.
Milgram therefore determined that individuals will obey authority figures even if it means causing harm to others. He believed that this experiment would help understand and explain why so many individuals i.e. the Nazis committed such heinous crimes against humanity during WWII.
From this, futher experiments of this nature were carried out and the one that I find even more incredulous and actually quite terrifying is the one carried out by Hoffling in 1966. This involved an experimenter impersonating a doctor and telling 22 nurses to administer lethal doses to a patient. Out of all of them, only one refused to do so.
Obviously they were stopped before they administered the lethal dose but I still find it terrifying that nurses with medical knowledge would be prepared to go through with it all because an authority figure told them too!