Role Playing Game. Although it's not quite what it's real life counterpart is - they're usually a far cry from Dungeons and Dragons. Wikipedia has some information. Generally RPG games are those that tell a story from the perspective of the character you control, and your actions within the game dictate the way your character deals with situations. But a lot of RPGs fall short of this goal.
Oh, and RPG is also Rocket Propelled Grenade, in the more warlike games. |