Not usually. Depends on the game though, I think that I do it if there's for example flying involved. I'm not sure why it's that that makes me need it though...
But when simply looking with a character, I guess I don't think about it like head movement but more like eye movement.
(Edit): BTW, I also have one friend that I know about (though I don't really have many gamer friends) that always inverts the Y-axis.
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