Money from Beatles record sales helped fund the invention of the CT scan (also known as CAT scan), a medical tool used to take three dimensional photographs of the insides of people's bodies.
As recounted on the blog Epidemix, the story starts with Godfrey Hounsfield, a researcher at EMI back in the 1950s. Although it's a (somewhat struggling) major record label today, EMI--which stands for Electrical and Musical Industries*--was once an industrial research company. Hounsfield did some pioneering work on computers, helping to build the first all-transistor computer, but the division wasn't profitable for EMI and the company sold its computer business in 1962...right when it signed The Beatles. His standing was good enough with the company that they let him conduct independent research with funding from the Beatles' string of massive successes in the 1960s. He went on to invent the CT scanner, which EMI first released in 1972, and shared the 1979 Nobel Prize for medicine for his invention.
I was aware of EMI's scientific legacy from a class I took on audio production: the company's Abbey Road studios (where the Beatles recorded) were legendarily cutting-edge, and an EMI scientist, Alan Blumlein, invented a microphone technique for stereo recording that's still used today. By the end of the 1990s, however, EMI had sold its technology businesses, and today it's exclusively a label and publisher.
*Corrected from "Electrical and Musical Equipment" which indeed would have made the acronym "EME." Whoops.