With me, it depends. I often like to make a world-appropriate character and role play it. It's strange, but I more often play as "Myself" when they put me in an already existing character that has freedom of dialogue and decision. Like in Mass Effect, and more recently Planescape: Torment (Anyone who wants an incredible story, play this now,) Commander Shepard and The Nameless One were both ME, how I would handle these situations. In Skyrim, though, Garsvald (The Nord of Destiny!) does whatever Garsvald wants. If a wandering minstrel gets in Garsvald's way, then Garsvald lets Garsvald's fists do the talking! Garsvald speaks in the third person for some reason, also. In Fallout, New Vegas, Mr. Clive Wyatt was a raging alcoholic who didn't trust them fancy techno-shooters, and would never EVER take off his signature hat for any reason. In Dragon Age: Origins, Murin was a Dwarf who didn't let his crappy past or his facial tattoo make him stop believing that people can be better than they often act, that only a little kindness was needed to show them the better way.
I don't know why, but when they leave me free to create 100%, I make my own new life, but when they give me a half-established character, I just sort of mold it around the guy I actually am.
I don't know why, but when they leave me free to create 100%, I make my own new life, but when they give me a half-established character, I just sort of mold it around the guy I actually am.