I think that it depends on the time and mood. Sometimes I get really into character when the mood of the table, the DM and the other players cooperate.
Other times, we just can't stop laughing about a joke that has nothing to do with the game.
I think the reason is because most of the time I play RPGs to escape from real life, to feel larger than life, to do things I couldn't actually do in real life. So, when the role playing consists of dealing with interpersonal relationships, love, anger, or any complicated emotion, I find it is no fun to try to role play it. I have enough problems with these things in real life, I don't need to deal with them in games as well. The same thing holds true for mundane things like buying things at the store, getting an inn room, etc.
In short, I want to be the fighter capable of killing 15 enemies at once without a scratch, who can lift a cart by himself, or the wizard who can kill his enemies with just a couple of gestures. That is the part of the role playing I focus on. Still, I want it to be fun and fair for everyone. So, because of that, during battles I concentrate on battle postitioning, the health of the group, how much damage the enemy has taken, etc. My character would be interested in that as much as I would, he just sees it in different terms than I do.