Strange to have thought of this right now, although I think it was a result of seeing Madonna dance around while singing "Open Your Heart." I used to have these completely non-sexual dreams about Madonna and myself, ourselves best of friends, hanging out clothed in bed, and engaging in girl talk (or philosophy, depending on the dream). In some cases, I would wake up, unaware that she wasn't in the room with me, sometimes for up to a few seconds.
This lasted for much of 1991 and some of '92, right up until the point at which I purchased her "Sex" book, after which time the dreams left me forever.
Of course, I have plenty of theories about what any of this means, especially in hindsight, if in fact they mean anything at all.