Gin rummy was a card game.
The rules were detailed in the book 1001 Popular Games Down Through the Centuries. In 2267, the USS Enterprise crew had grown quite tired of this game. (TOS novel: Mission to Horatius)
In 2375, Vic Fontaine offered Quark the chance to play a game of gin rummy, although he was not keen. (DS9 episode: "What You Leave Behind")