I suppose for me it's a game where the player has a great deal of control in how to improve your base character(s). I don't think it has to strictly be stat based (I still count Deus Ex Human Revolution as an FPS/RPG) but it shouldn't be solely tied to in-game progress and there should be multiple elements you can improve/develop as you progress. For instance, the hearts in Zelda are for the most part, a result of game progression, or the in original Metal gear Solid where your health increases after defeating each boss; I don't count either of these as RPGs.
However, I also feel that storytelling should play a bigger part in defining what makes an RPG. The ability to influence the storyline is usually associated with adventure games, but to me this also makes a significant portion of what an RPG should encompass; shaping your character not only in battle stats, but also in character/personality development. In games with a party system, this should include inter-party relationships.
IMO combining both elements (stat increases and character development) is what makes a truly great RPG.








