In our LARP setting, most of the world was conquered by a particular power about 750 years ago, who then ruled for about 250 years. So there was plenty of time for the language to become the standard for governance and trade. Much like Latin, though more recent. Other languages are less used, although they still shape names, accents, etc. It's convenient for a LARP.
For our table-top game, there's no common tongue. There is the language of the kingdoms where most of the game takes place, but that only seems "common" to us provincial types. Most of the characters know multiple languages, but only a few are known by all the characters (possibly only one). I think it's good for a table-top game because it shifts who will speak for the party depending on the circumstances.