Mario and Luigi hit the links in Vs. Golf.
This arcade game was released by Nintendo in 1984. This game was known as Stroke and Match Golf in Japan (and the MAME emulator uses that title as well). There is also an alternate version of the game (known as "Ladies Golf"), that has young women playing (instead of Mario and Luigi).
This was one of the first Golf titles ever released in arcade format. It set the standard for the golf based arcade game. Most golf games to come later were merely copies of Vs. Golf with better graphics. Even the latest Golden Tee golf games are almost identical in control and gameplay (although they have opted for a trackball over a joystick).
The game requires little instruction for anyone who has ever played a golf game before (there is a little sequence you can watch that explains things, if you need to know them). This is all basic stuff, choose your club, aim your golfer, and swing (it uses a power meter system to determine the length of a swing).
There are 18 holes, most of them well designed and fun to play (you get 3 holes for every quarter you drop in the coin mech). But a couple of the holes are exceedingly difficult, and require tee shots to small areas at odd distances from the tee. This game is best played in 2 player mode, and is rather slow paced, so it is quite relaxing when played in that manner.
Guess what? I have one of these. This was the first arcade game I ever owned. It currently shares a cabinet with my Vs. Super Mario Bros. game. I changed the machine's marquee over to the one for SMB, but the two titles used the same control panel. This is a Nintendo Vs. Unisystem game, which means it can be easily converted to other Unisystem games by simply swapping the mainboard (or you can do what I did, and mount several mainboards in a single cabinet, and just move the harness from game to game). The Vs. Unisystem was designed to retrofit old Donkey Kong and Donkey Kong Junior machines, so that Vs. Golf machine you are playing probably used to be a Donkey Kong. My machine was originally a Donkey Kong 3, which was the least successful of the Donkey Kong series.
This title was also released for the Nintendo Entertainment System under the name of Golf (graphics are slightly different, otherwise it is identical).