With my main experience with the genre being Zelda, Final Fantasy and other Square titles through World of Warcraft, RIFT and SWTOR my loose definition of RPG is:
The grind of stat growth through the acquisition of experience points/ability points/action points/JP/etc, currency, reputation, gear, spells/abilities, transportation and/or ranking to pursue the goal of eliminating the strongest bad/good guy.
My definition probably leaves out many of the sandbox-type games that I have never played. It also assumes it is all about the quest to increase stats. Connections to one's avatar, comrades or even the story are completely absent from my definition.
Please share your definitions and understandings of what the RPG genre is about.
I do wonder how much of a future the "stat grind" I mention has. Obviously it has persisted since the old tabletop/pen and paper RPG's before video games were around.