The Spanish Inquisition was an event that occurred in Spain, intended to convert the Jewish and Muslim inhabitants of the country to Christianity.
In 2286, Dr. McCoy's view on primitive 20th century Earth medicine, including the use of image therapy and radical chemotherapy as the only means of an ailing patients survival, was less than positive. After hearing that two doctors at Mercy Hospital had an argument over the issue, McCoy stated that the whole scenario "sounded like a goddamn Spanish Inquisition" to him. (Star Trek IV: The Voyage Home)
In 2369, Q told Vash that he believed the Spanish Inquisition to be, along with the Crusades and Watergate, to be one of the most interesting events to happen on Earth. (DS9: "Q-Less")