The most playoff holes played in golf was 72 holes at the 35th US Open Tournament between Von Elm and Billy Burke in 1931.
The two players tied on 292 after they shot 72 holes. The tournament had to be split into two days, where the two golfers scored a 36 hole playoff on the first day, and the same on the second day.
At this time in golf history, there was no sudden-death rule. This meant that they had to go through the playoffs all the way. Billy Burke won with 148 over 149.