SkeleTony: Well, I don't want to come off as arguing that one type/style of game is better or worse than another but your above is a bit erroneous as far as RPG definition goes and is also a false dichotomy(re: stats, in many well designed RPGs determine a whole lot more than how good you are at "killing stuff").
RPGs by definition have to be heavily stat-based. Without those quantifications then you are left with either no GAME at all(just improvisational acting/drama class) or a completely different genre of game(such as arcade-action or adventure). The thing that differentiated D&D(as badly designed as that game was, it was still the original RPG) from "Cops and Robbers" or "Cowboys and Indians"(two role playing activities that were common to young children up until the 1980s or so) was that "Cops and Robbers" ALWAYS degenerated into arguments between the kids of "I shot you!"/"No you didn't...I ducked behind this tree!/No I shot you before you moved!/etc." Why? Because there was no GAME mechanics. No means to measure one person's probability of shooting the other or avoiding being hit by the other etc.
RPGs are special because they have quantified game mechanics(i.e. "stat based gameplay"). This does not preclude(in fact it encourages) choices and consequences, storytelling, acting etc.
You're quite welcome to argue that one style of game is better provided you remember it's subjective.
To clarify my opinion, I'm not doubting the need for stats in a RPG, I actually prefer when the game gives a detailed explanation of its mechanics, how things work and have complex stats and derived abilities. I like numbers, provided they make sense and are explained properly somewhere.
However, I find that in many recent RPGs, contrary to older games like Planescape Torment, Fallout or Arcanum, your base stats have very little influence on anything except combat ability. How intelligent, or how charismatic your character is often makes no difference at all to how the game plays out for you, except in combat (depending on class) and possibly in some conversations.
That obviously makes very little sense in a RPG that's by definition supposed to rely more on character skill than player skill to determine what you can and can't do. A very clever character should be able to find alternative solutions to quests, a very charismatic one should be avoid to avoid some fights with intelligent enemies, etc...
I also didn't mean that a game that doesn't do that type of thing (like Morrowind, for instance) isn't an RPG, just that I'll like it less than one that makes the effort of making the game reflect what kind of character I'm playing in other areas than combat, therefore increasing replayability. This is why I like stat checks, both in conversation and for quest options.
