Stanley may be the most recognized name, for a couple reasons like the free publicity Stanley get from the carpet cleaner company, Jay Leno's occasional talks, and the land speed record a Stanley set for steam powered cars that stood for 103 years
But others like Doble did a good business, Locomobile was seen frequently in early movies, one presidential limo was a White steam car http://justacarguy.blogspot.com/2007/06/presidential-limo-circa-1909.html , Toledo made a name for themselves during endurance races against gas powered cars, and other small companies like the Leyland in the last photo were using steam engines for some reason or another, perhaps lack of gasoline in areas
In 1906 the Land Speed Record was broken by a Stanley steam car, piloted by Fred Marriot, which achieved 127 mph (203 km/h) at Ormond Beach, Florida. This annual week-long "Speed Week" was the forerunner of today's Daytona 500. This record was not exceeded by any land vehicle until 1910, and stood as the steam-powered world speed record till 25 August 2009.
Stanley steam car (1912)
Attempts were made to bring more advanced steam cars on the market, the most remarkable being the Doble Steam Car which shortened start-up time very noticeably by incorporating a highly efficient monotube steam generator to heat a much smaller quantity of water along with effective automation of burner and water feed control. By 1923, Doble's steam cars could be started from cold with the turn of a key and driven off in 40 seconds or less
Abner Doble developed the Doble Ultimax engine for the Paxton Phoenix steam car, built by the Paxton Engineering Division of McCulloch Motors Corporation, Los Angeles. Its sustained maximum power was 120 bhp (89 kW). The project was eventually dropped in 1954.