Boxing, or pugilism, was a sport in which two participants of similar weight fight each other with their fists. Victory was achieved if the opponent is knocked down and unable to get up before the referee counts to ten (knockout) or if the opponent was deemed too injured to continue (technical knockout). If there is no stoppage of the fight before an agreed number of rounds, a winner is determined either by the referee or judges' judgement.
In the 1950s, Benny Russell, Willie Hawkins and Cassie Johnson were fans of boxing. While Hawkins participated in the sport, Russell and Cassie would listen to matches on the radio. Cassie hoped that one day there would be a chance for women to take up boxing. (DS9 novelization: Far Beyond the Stars)
Sven "Buttercup" Hansen, an ancestor of Seven of Nine, was a prize fighter during the 22nd century. (VOY episode: "11:59") The captain of the ECS Bjarni Herjolfsson was a great fan of Hansen and, consequently, named Hansen's Planet after him when his ship discovered it at some point prior to 2163. (ENT - Rise of the Federation novel: A Choice of Futures)
In 2369, Q challenged Benjamin Sisko to a boxing match after Sisko demanded that the entity return the Deep Space 9 residents who had disappeared. Q began hitting an unimpressed Sisko, who threw a punch of his own, knocking Q to the ground. (DS9 episode: "Q-Less")