I have dreamed (hmmm, catchy...) some exquisite little musical moments, ranging from symphonies to Broadway scores. One I'll always remember -- well, not all the details, but the fact of the dream remains -- is having been reminded of, or introduced to, the "lost music" to CAMELOT. I'd just been given the "special" score that contained all of this discarded or lost music and it was twice as thick as the printed vocal score, and I was opening it up and chomping at the bit to start studying it when, naturally, I woke the f up! But the song "Before I gaze at you again" was somehow a key to discovering this lost material (whatever that means; it just was), and that played in the dream, and echoed in my head throughout the next day.
I've certainly had single phrases like the "Piddle Twiddle" one take over dreams and stick with me as well.