This widely anthologized short story classic was written by Richard Connell and first published by Collier's Magazine on January 19, 1924. Sometimes this story is titled as "The Hounds of Zaroff".
Why the change in title? Well, the answer has to do with the different denotations of the word game.
This story has been adapted over eight times in a variety of mediums: Richard Bachman's book The Running Man recreates it. Orson Welles did a radio adaptation. The 1932 film version is in the public domain and the most recent film version was released in 2008.
There's even a vaporware adaptation of it. More tangentially, check out Smokey Robinson's song "The Hunter Gets Captured by the Game.
In addition to the game which SabreCat describes, Connell's story is also credited as the inspiration for paintball.
Why is this story so popular? Well, it has become an archetype of a particular form of conflict and an exemplary illustration of situational irony. It has fully entered the cultural consciousness to the point that Gilligan's Island and Charlie's Angels both did episodes which use this trope.
You probably read it in school. If you didn't, you should go read it now, as it's a pretty good yarn.
Go ahead. I'll even give you a head start.