This is the definition I've gone by for many years...
What separates RPGs from other games where you "play a role" is all in the telling of the story itself. While we may think of "experience systems" and the like defining the genre, it's not the only basis. An RPG is meant to be a "novel". In a novel, the main focus of the story is on the character or characters, and how they change. An RPG is the same...focus on the characters and how they change throughout the story. Other games tend to focus on the story itself, making them "short stories" (it doesn't mean the story itself has to be short, it's a literature term to describe a story that's based mainly on events rather than focusing on its characters). With this in mind, the early Zelda games cannot possibly be called RPGs, because the focus was never on Link, but on the story around him. Games that we all know to be RPGs...take a close look at them...there's usually very detailed character development. Ironically, this definition makes it difficult to consider the original Final Fantasy an RPG...the main focus is on the story, and there's very little character development. The only thing that could save its bacon is the fact that the characters do in fact change at one point. But that's truly grasping for straws, and I've considered Final Fantasy to be an adventure game for a long time, NOT an RPG.
This is the only definition that cannot be countered. Any other definition can easily be countered, and you end up right back where you started..."all games are RPGs because you play a role in all games".