Assigning a persona to your character in, say, Morrowind or Oblivion is all well and good, but if the game doesn't support that persona, there's not much of a role to play. I found that in Morrowind it hardly mattered what you perceived your character to be, interacting with NPCs was so painfully dry and utterly un-engrossing, there was no role-playing at all.
I don't know if Oblivion is any better in terms of supporting different personas, though I somehow doubt it very much.
To really be able to play a role in a single-player RPG, the game has to support different moral and ethical choices, and have consequences and meaning to those choices.
Out of the RPGs I've played in recent times, the only ones to really go in that direction are the Fallouts and Planescape:Torment.
Knights Of The Old Republic 1 and 2 aren't too bad, but BioWare have a tendency of Butt-Kissing Good, Apathetic Neutral or Arsehole Evil, not really offering much in the way of different aspects of those alignments.
There are worlds out there where the sky is burning. And the sea's asleep and the rivers dream â€¦ People made of smoke and cities made of song â€¦ Somewhere there's danger, somewhere there's injustice, somewhere else the tea's getting cold!