In the United States between 1920 and 1939, depending on the area. In the cities, cars took over after Henry Ford. Many cities banned horses because of manure and dead animals left in the road. When the Depression finally ended in 1939, most of America discontinued their use of horses for good and used the gas-powered cars only.
By 1929, states had gas taxes, which funded roads. In all 48 states, D.C. and municipal codes separated residences from businesses and made off-street parking a business requirement. It wasn't until after World War II that the idea of personal car ownership became part of the staple of the American dream.