The most notorious is probably the British GP Harold Shipman, who killed at least 218 of his own patients according to an extensive investigation. He started out killing elderly women who did not have a long life expectancy, and perhaps he told himself he was acting out of mercy. But as time went on he relaxed his standards and started killing perfectly healthy people. He did it during house calls by injecting an overdose of heroin, which is used legally in the UK under the name diamorphone. He was only caught because he crudely forged a will of one of his victims to get her estate. Possibly at some level he wanted to be caught.
Donald Harvey was a nursing aide who plead guilty to murdering 37 people in Kentucky and Ohio but likely killed many more. He said these were mercy killings but he also murdered an ex-boyfriend and other acquaintances. It is particularly disturbing that he used a variety of methods, which were generally not as hard to detect as heroin or insulin overdoses. He used a variety of poisons, also smothered people and sometimes just let their oxygen tanks run out. The doctors were too busy to suspect anything, apparently.
Charles Cullen was a nurse who confessed to 40 murders but is thought to have committed up to 400.
Astonishingly, he continued to work as a nurse after his first employer, St. Barnabas hospital in Livingston, New Jersey concluded that he had contaminated IV bags, resulting in the deaths of dozens of patients. He continued to face allegations and suspicion of harming patients at various hospitals but continued to find employment elsewhere for several years. As Wikipedia states,
Cullen was largely able to move from facility to facility undetected because of the lack of requirements to report on suspicious behavior by medical workers, and inadequate legal protection for employers. New Jersey and Pennsylvania, like most states, required health care facilities to report suspicious deaths only in the most egregious cases, and penalties for failing to report incidents were minor. Many states did not give investigators the legal authority to discover where a worker had previously been employed. Employers feared to investigate incidents or give a bad employment reference for fear that such actions might trigger a lawsuit. According to detectives and Cullen himself, several hospitals suspected he was harming or killing patients, but failed to take appropriate legal actions. Following Cullen's criminal conviction, many of the hospitals where he had worked were sued by the families of his victims. The files and settlements against the New Jersey hospitals, all settled out of court, are sealed.Michael Swango, a physician who is thought to have murdered as many as 60 people, also managed to continue to find employment even though nurses had noticed that is patients kept mysteriously dying during his internship. The hospital did a cursory investigation and cleared him, but did not allow him to enter his second year. He got a job as an EMT, at which he started poisoning his co-workers, for which he was convicted and served 5 years in prison. He then used forged documents to get a job as a physician in South Dakota. The poisoning conviction was eventually discovered and he was fired, but he then managed to get a job at the VA medical center in Northport, New York, where again his patients started mysteriously dying. After his past was once again discovered, he fled to Zimbabwe where, you guessed it, he got a job as a physician. Eventually authorities tracked him down and arrested him in a layover in Chicago while he was on his way to Saudi Arabia. (FYI he is currently living out his years in the Supermax.)
What these and many other cases have in common is that these are individuals who simply enjoyed killing people, and as medical providers they were in a position to do it often and without detection. They were aided by institutional aversion to learning inconvenient truths and doing anything about it. Physicians are granted extraordinary power. They can stick their fingers up our asses and into our vaginas, if we have one. They can also cut us open and remove vital organs, and inject us with toxins. It's obviously rare for them to be psycho killers but we don't actually know how rare.