Mario Golf is a series of golf videogames by Nintendo, sub-series of the Mario series.
Mario first starred as a golfer in Family Computer Golf Japan Course and Family Computer Golf US Course, released in 1987, but those aren't technically part of the Mario series, and are instead part of the Golf (Nintendo) series.
The actual golf games with Mario in their title are:
Mario Open Golf (September 20, 1991), known outside Japan as NES Open Tournament Golf. Re-released in 2007 for Wii Virtual Console and in 2011 for 3DS Virtual Console. Being yet another game in the Golf (Nintendo) series, it's sometimes not considered an actual part of the series.
Mario Golf 64 (June 11, 1999), Nintendo 64. Simply called Mario Golf outside Japan. Re-released in 2008 for Wii Virtual Console and in 2015 for Wii U Virtual Console.
Mario Golf GB (August 10, 1999), Game Boy Color. Simply called Mario Golf outside Japan. Re-released in 2012 for 3DS Virtual Console.
Mario Golf: Toadstool Tour (July 28, 2003), GameCube.
Mario Golf: Advance Tour (April 22, 2004), Game Boy Advance.