The Bloody Benders
This was a family of serial killers that owned an inn and general store in Kansas, between 1871 and 1873.
The family consisted of John and Elvira, and their son John Jr and Kate. According to the rumours, however, none of them were related and they were all posing as a family for their sick habits.
After the authorities found that several travellers had checked into the Bender Inn, but never checked out, they started to investigate. All they found were bodies, and no sign of the ‘family.’
You forgot Harold Shipman, probably the world's most prolific serial killer and a doctor.