What a great question!! I sing along in my head. Well, actually, I have to MAKE myself sing along and really, really listen. Otherways I just float away as others mentioned: my grocery list, how soon can I eat (I can't eat before a concert, so as soon as I relax a little, I'm starving), did I put away the bread so the dog can't get it etc. I also think about a few teachers who really inspired me and if they would like what I'm doing right now. Usually I think they wouldn't, they would know I'm thinking about all these other things... Sometimes I drift long enough that when I come to, I'm two pages farther than I expected. Not good! I don't like to go on auto-pilot, I really do want to stay in the moment, but it's a bit of a fight.
To Pianonut and the piano-for-exercise question: I guess some people would have a negative response to that, because you're not going deeply into the music in that kind of playing. But I think playing can mean whatever it means to you at that moment. There is definitely a tactile pleasure in playing an instrument, and maybe it's enough to just enjoy that sometimes for its own sake. About being bored, whenever I'm getting ready for something, my teacher and a few friends ask me if I'm bored with the music yet. I usually say no, and they say that means I haven't practiced enough! So maybe you're just incredibly well prepared.