Of all the multiplayer modes available for a game, PvP (Player VS Player) is one of the most appreciated. The thrill of competing in some way against a human opponent is something that changes the way you're playing and is often completely different than fighting a computer opponent. In fact, the first games in history lacked a computer opponent (it needed more resources, more code, etc.), there was PvP before everything else.
Some of the most popular abandoned "PvP (player VS player)" games: