Fencing was a sport from Earth that involves two competitors, wearing protective clothing, engaged in combat with a foil, a thin, blunted sword-like weapon. The goal of the competitors was to score points by making "touches" with the foil on the opponent's body. The first competitor to reach a set number of points was declared the winner.
Hikaru Sulu was an avid fencer and once described himself as a "master swordsman". While affected by the Psi 2000 virus in 2266, Sulu chased crewmen around the corridors of the USS Enterprise with his fencing foil.(TOS episode: "The Naked Time"; TOS - No Compromise comic: "Part One")
In an alternate reality, Sulu had received advanced combat training in fencing. In 2258, he fenced with Romulan guards atop the Narada's drill platform high in Vulcan's atmosphere. (TOS movie: Star Trek)
Shortly after being assigned to the Enterprise in 2267, Ensign Pavel Chekov decided to take up fencing, and for a while he would practise against the ship's computer. However, after some goading from Sulu and Nyota Uhura, Chekov decided to practise against Sulu. (TOS - No Compromise comic: "Part One")
Captain Jean-Luc Picard was also a keen fencer and faced a number of competitors during his time aboard the USS Enterprise-D, including Commander Riker, Lieutenant Dean and Guinan. Captain Picard also had a duel with the USS Hood's Captain Robert DeSoto.(TNG episodes: "We'll Always Have Paris", "I, Borg", "Lessons"; TNG - Terra Incognita comic: "Issue 2")