There's no right or wrong answer here, mostly because it depends on your first and favourite RP experiences. So I'm just going to post how I feel a roleplaying game should be defined.
1) Choice. I remember seeing a commercial where it said "or is a bore", and since then it's stuck to me like sellotape. Being able to choose what race and class my character is, their history, their intentions, their morale alignment, their personalities, their homes and their features. I want to play the role of something, hence why I am playing a role-playing game. I want my character to be *my* character, and not someone else's.
2) An expansive world rich with lore. I want my character to be in an environment where he has the option to explore, and see every single thing. TESIV: Oblivion is a near-perfect example of being able to go anywhere and do literally anything without any level requirements - the world is your sandpit and you're free to do what you like in it.
And that's all I can think of thus far. RPGs are the king of endless joy and exploration, both of character and of world. There's no such thing as a linear RPG; there's no such thing as an RPG with no character development elements. Those games are just adventure romps and they sicken me.