First golf game I ever played was on the Apple IIe - it was quite a neat game as tt generated a new course every time you played. It was only 2D overhead and the graphics were basic and pretty lo-res but it got the job done. The gameplay was excellent and rewarded practice and skill and supported the Apple paddle controller.
It was just called Golf - no idea who developed it - it may have been a sample AppleBasic program but we got hours of entertainment out of it in multiplayer at school breaks.
Golf is always great in multi-player and it is perfect hangover Sunday afternoon gaming - used to have loads of fun with my mates on Arnold Palmer Golf on the Megadrive, I can also remember great times playing the old NES Golf game on a Playchoice 10 which required real judgement as you only ever knew the total length of the hole - not how far to the pin you had to go - so it required real skill and knowledge of the game. Great fun in a pub environment.
Always liked Leaderboard - played an old DOS version in work quite a bit when PCs first showed up (was a green screen programmer back in those days). Also have world class Leaderboard for the MD. I had forgot how the putting angle was shown in that game - quite original really.
Was never that fussed on PGA golf - especially later games that just added too many gameplay aids and made it feel too contrived - though I quite like Tiger Woods games on Wii that support M+ - loads of content in those too. (Frisbee mode is fun too!).
Mario Golf on N64 (and GC which looks gorgeous and irons out the N64 game) is excellent too - still enjoy that when I just want to play some old 3 press system golf and sit on the sofa.
The basic Golf game in the old Gameboy was a lovely little game too - excellent control and really effective use of graphics.