The thing that really makes an RPG for me is if it is able to get me to make decisions that aren't optimized for the maximum possible gain to my character.
In other words, if I can get a huge stockpile of weapons, supplies, ammuniton, what-have-you, and all I have to do is murder some people, the game has to be convincing enough for me to value playing as a non-kleptomaniac mass murderer, and for reasons other than "if you steal and kill the game will repeatedly fuck you over/NPCs will try to kill you". So if I feel bad enough about killing these virtual characters that I decide to do the >right< thing rather than the >profitable< thing, simply because I don't want to kill them, it is doing things right.
For the vast majority of RPGs, NPCs simply aren't characterized well/deeply enough for me to care more about them than whatever loot or stat increases can be gained by not caring about them.
Interestingly enough, it isn't RPGs that tend to evoke this reaction from me the most, it is strategy games, both 4X and realtime. I find myself caring enough about individual units that I will spend (not waste) time that could be spent maxing out my research and construction rates microing a rescue force across the map to help them out; when I play against computer opponents I often find myself setting up defenses that run themselves and then having fun building stories with small groups of units. For 4X games, one of the most notable tendancies I have is in Aurora, I follow officers up through their careers, deploying entire fleets to scoop up their lifepods when their ships are destroyed, etc. And I don't do this for in-story fluff for a LP, I do it for fun.
I think a big part of this is that when the 'character' as such is largely abstract, I am able to project a personality on it, in much the same way that I do when building an identity for a PC in a RPG; I try to play the character the way it should be played, but as the PC is often the only sympathetic character in many RPGs (largely because it is the only one with a fully-developed personality, as the player is actively supplying that), this tends to devolve into every character being the aforementioned kleptomaniac mass murderer, because that tends to be the most effective at furthering the aims of the character.
So essentially, for me a successful RPG is one which makes the PC (i.e. the player-driven personality) care about other characters, even when doing so is detrimental to their own success and profit. Basically, it needs to be able to evoke compassion, remorse, protectiveness and other strong positive emotions in the PC in much the same way that they are evoked in most real humans.
And that, in turn, makes violent klepto PCs in RPGs which successfully do that the virtual equivalent of bankers and stock traders.