Great topic.
I think there is a lot of disagreement over this subject. Here's my own definition, for what it's worth.
An RPG is a game that features 1) a set of tangible, appreciable statistics that directly correspond to intangible qualities like strength, charisma, and wisdom, 2) the ability to modify those statistics by earning experience points by defeating enemies and completing quests, and 3) the electronic simulation of die-rolling mechanics from pen-and-paper RPGs like Dungeons & Dragons to determine success and failure.