Getcomposted: My ultimate definition of an ARPG depends on how it makes me feel. An ARPG makes me feel energized and in battle, especially melee battle with a multitude of enemies coming at me, it makes me think, "I'm gonna die.. I'm gonna die.. Die! Die!"
Of course, there is one battle in the original Bard's Tale where you have to fight 396 melee enemies at once, and that game would definitely not be classified as an ARPG, as the game is turn based.
(Then again, the most practical way of winning this fight is to use spells and breath attacks to take out groups of enemies at once, and then raise the battle message speed as high as it will go, even if that makes the messages go too fast for you to read.)
Might and Magic 2 also has some huge encounters, and many times the easiest strategy is just to cast Power Shield and then auto-attack until the battle is over (assuming your party is strong enough).
Getcomposted: My first RPG (as I see it) was Eye of the Beholder on the Amiga, and thus Dungeon Crawlers are definitely RPG's in my book. My first CRPG in the strictest definition of the word, in that I played it on a PC, was Planescape: Torment.
I'd argue that Eye of the Beholder was your first CRPG, as it is an RPG that is played on a computer.
Now, if you had played Dungeons and Dragons (with pencil, paper, and other players and a DM), now that would be an RPG that is not a CRPG.
tinyE: This is a silly question and maybe I'm a big dork for feeling strongly about this, but what about aesthetics? Along with choice for build I like a lot of choice of look, and more important, when I get items and use them, be they armor, swords, or even just a ring, I WANT TO BE ABLE to see them on my character.
Gilozard: Aesthetics are definitely an important part of character customization. Not all RPGs have much of it due to POV limitations or something (ex, Legend of Grimrock), but most of them try to have at least some of it.
And RPGs don't have a monopoly on that feature. Consider such games as The Sims and its sequels, which I have never seen be referred to as RPGs, but which definitely allow you to customize your character's appearance.
(In fact, I believe that in the newest installment, a patch removed some of the restrictions on character customization, allowing you to even create a character who appears and dresses male, but can become pregnant, for example.)