You make a party of different characters, each with their sets of skills and abilities. And these sets of skills and abilities determine how well they perform in those tasks, not yours as the player. Obviously this defines how you handle the encounters and might force you to develop different strategies. And yes, here you play a party of characters but it's not as if you have to control only one to have a CRPG.

Well, you did say "a specific character," after all.
So you're defining an RPG as a game in which the player makes decisions about the character(s) in some capacity, and in which those decisions impact gameplay?
I'm not trying to harrass, I'm just curious.

Mass Effect
The Witcher
Neverwinter Nights 2
Jade Empire
Baldur’s Gate II: Shadows of Amn
Fallout 2
Close Calls:
Morrowind
Planescape Torment
S.T.A.L.K.E.R.
Deus Ex
Dungeonsiege 2 ((bite me i love this game))
Diablo 2
Thats my top 5... and as for Gothic 3 i feel its a worthy contender that trumps Two Worlds on playability... only AFTER the latest community patch... But i do not agree with Fable, its an action game more then an RPG.. it doesn't pull you in or give you any immersion....

Makes sense. Whether related to the story or just pure gameplay, you influence how your characters turn out.
Do JRPGs count? Some let you make decisions like this, but many, especially the older ones, give you little if any freedom.
Final Fantasy IV is a good example - you have no control over the story, the dialogue, or the makeup of your party, and character advancement is entirely automated; you don't get to decide what stats to increase, what spells you learn (aside from a handful of optional bosses that give Rydia new call spells), what weapons you can equip, etc. Pretty much the extent of the impact you have on your party stems from your ability to find better equipment, and how much time you spend grinding experience levels.
Interestingly, the first Final Fantasy is probably suitable, because it plays more like a traditional crawler. Party interactivity is probably a notch below the earlier M&M games, but you do create a party of four from six possible classes, and the composition of your team has a huge impact on how the game plays (I had great success with fighter / fighter / black belt / white mage). You also have to decide which spells to teach your casters, as no one character can learn all the spells in the game.

The old FF game were really influenced by other dungeon crawlers. Wizardry was also extremely popular in Japan. The serie, and other jrpg for that matter, moved away to focus more and more on the story, which is usualy not too good.
Problem with the whole genre is that now it often forces you to sit through a shallow story, gives you no control at all over your characters, and throws lots of unchallenging fights your way, which is a bit counter-productive if the main appeal of the genre is the story and all it does is prevent you from getting to it. Still there are a few gems here and there.

Yeah, you can see the influence of early western RPGs on games like Dragon Warrior and Final Fantasy. I think the DW guy in particular cited Wizardry as one of his major inspirations. I think it's interesting to look at the common roots of different types of modern roleplaying games, and see how they split off and evolved in different directions.
Would you say that such games don't count as RPGs, then, or would you say that there are just a lot of RPGs "done wrong," kind of like how a lot of movies that get placed in the action genre and marketed as such actually don't have very much action at all?

For the sake of simplicity, I still consider them as part of the RPG genre. Besides as I said before, just putting RPG next to the name of a game won't instantly make it better or worse than it actually is. Plus in most cases, if they have some semi-decent combat, you have to juggle with the specialties of different characters. It's light but I'd say it qualifies.
I guess it helps to have some core definition of RPG, because from there you can develop the sub-genres, or even mix RPG elements with other genres (think of King of Dragon Pass, an awesome blend of 4X games, like Civilization, with RPG elements). Else for some people only games with very heavy stories (good or bad is another question) qualify as RPG, for others it's only the old-school dungeon crawlers. In the end, it's only a way to classify stuff and maybe help to compare games to each other, but it tells nothing of the intrinsinc quality of the game itself.

Fair enough. I agree, though, that it's a bit pointless to argue over whether a particular game is or isn't a "real" RPG. Classifications are useful (and interesting), but we're talking about entertainment media here - it's nearly impossible to draw hard lines between genres, and I don't think it's especially helpful to do so, anyway.
Now, if they put Tetris and Painkiller on that list I would probably question their sanity, but what's on there is close enough for jazz.

I also draw the line at games like STALKER: it really doesn't qualify as an RPG.

What's wrong with Fallout 3? Okay, it's not like Fallout 1 and 2. I love Fallout 1 and 2. But to say Fallout 3 is a bad RPG, to me, makes me think the person is speaking from Bias. I didn't care much about Fallout 3. But I liked it, it was a quality game, and it was fun. ~Shrug.~
I couldn't stand morrowind either, and prefer oblivion to morrowind, on the sole fact that combat in oblivion isn't as nearly as lame (but still feels lame to an extent.)
As far as best RPGs evar, let's just concede Baldur's Gate and Planescape rule then call it a day.

I do hope the first question was a rhetorical one....

It really wasn't. I enjoyed it. And this is coming from a Hardcore Fallout 1 and 2 fan (I guess it doesn't matter I keep saying this.)

Alright, I'll bite. I am a fan of the first two Fallouts myself. I am not NMA hardcore about it, but I do like certain things in my Fallouts.
Lack of turn-based combat. Sorry, but Bethesda making it into an FPS with RPG elements just doesn't cut it. The stats in the game appear to be nothing more than decoration. Also, they truly butchered the lore of the Falliuts by introducing Jet on the East Coast when only ONE person knew how to make the stuff and he sort of ceased to be. In essence, it feels like they just picked some things out of the corpse of the franchise while leaving the stuff that made it an awesome franchise on the corpse.
Dialogue, dialogue, dialogue. FO3 has dialogue that could have been better written by a neutered cornflake. Read the dialogues of the first 2 Fallouts and compare them to the third and I am sure you will notice a severe difference in the quality of writing.
They also used Oblivion's engine along with the Radiant AI. Let me tell you something about Radiant AI. This is the same AI that had characters raking their carpets in Oblivion...
All in all, I, myself, would have prefered to have the franchise dead rather than revived the way it is now.

I won't attack Bethesda for making Daggerfallout - I did my best to approach the game with an open mind, despite that it wasn't the Fallout 3 that I or anyone else wanted - but even taken on its own merit, I still have complaints about the game.
I felt that there wasn't much to it. For me, the game pretty much stopped at level 4 or 5. Over the next thirteen or so levels, I don't feel like I advanced my character in any meaningful way - I was fighting the same enemies using the same weapons over and over, earning mostly useless perks and mildly useful skill points. I ended up not finishing it - it got very repetitive, but maybe that's my fault for wandering too much instead of following the main story (but isn't the ability to do that part of the point?).
Aside from that, I found the NPCs to be extremely thin. Most of them just don't have much of interest to say, and as a consequence of that, your own dialogue is pretty threadbare as well. As I recall, Fallout 1 suffered from that a bit as well, but not nearly to this degree.
Many of the points of interest didn't have much going for them, either. Some of them were very cool; you could often find recordings or hack computers to get some backstory on the place and what was or is going on there, and some of the more unique locations were fun to explore in their own right. Others, however, were just generic buildings filled with junk I don't need.
I had fun with it for a few hours, most notably in Greyditch and in the supermarket outside of Megaton, but after that I felt like it stopped trying.