A house call was a visit to the home of a patient or client by a doctor or other professional. One snide nickname for EMH Mark Ones was "Extremely Marginal Housecalls". (VOY: "Life Line")
In 2267, Leonard McCoy joked that he was not going to be making any house calls on Spock after the Vulcan had increased the temperature in his quarters to 125 degrees. (TOS: "The Deadly Years")
The next year, when asked to board a Romulan ship for a medical emergency, McCoy stated that he did not make house calls. He changed his mind when told that James Kirk was the medical emergency. (TOS: "The Enterprise Incident")
In 2371, Tom Paris recalled that Doc Brown made house calls to his patients, including one to Paris himself when he was nine years old. (VOY: "Cathexis")
In 2372, Julian Bashir commented that he didn't realize that Trevean made house calls when the Teplan treated Ekoria at her home. (DS9: "The Quickening")
In 2375, B'Elanna Torres incorrectly assumed that a visiting Chakotay was The Doctor making a house call to her quarters. (VOY: "Extreme Risk")
Similarly, Captain Kathryn Janeway later thought The Doctor's presence on the bridge was another house call to get the captain to undertake a physical. (VOY: "Latent Image")
After saving the life of his creator Lewis Zimmerman in 2376, The Doctor told him that Janeway would be unlikely to authorize any further house calls. This was said as The Doctor had traveled thousands of light years to the Alpha Quadrant to treat Zimmerman. (VOY: "Life Line")
In 2399, Doctor Moritz Benayoun made a house call for Jean-Luc Picard to inform him of the results of his exam for a Certificate for interstellar service. He informed him he had passed every test except for a defect in his parietal lobe had developed further and the symptoms were fatal. Based on this he could not approve him for interstellar service. (PIC: "Maps and Legends")