I think, for an RPG to really be an RPG, you need a few factors:
1) Control over your own character's appearance, attitude, and (even loosely) control over your character's abilities and role within the game.
2) Interactions with NPCs that evolve over time, and are unique based on character input.
3) Your character's actions have an impact on the game world.
4) You have interactions with other players, at least in small amounts
So, with that said, most MMORPGs are *not* RPGs, in my opinion. You're fairly limited in just what your character can *be* (and one elven paladin is going to be more or less like every other elven paladin, down to appearance - when I played EQ for a bit, you could tell someone's class just by how they looked!). If I talked to an NPC, I got the same response as if you were to talk to the NPC, and the same output from said NPC. And, in an MMO, even if I killed King Gongbladder the Eighth, or whatever... he was back next hour - and wouldn't recognize me if I killed him again.
Now, some single player CRPGs fulfill all these criteria, except for the last- and if you are playing a game by yourself, I really think it's kind of missing the point. It's sort of like the difference between sex and auto-erotic activity - both can be fun, but...