Waterworld, the score starts very softly as the Universal logo plays, the words "Universal" then fade as the camera slowly moves towards the globe as water covers the land masses.
Transformers added transforming sound effects over the logos (I think they all do this but I know the first one does).
"Then He Kissed Me" begins playing during the Touchstone logo for Adventures in Babysitting.
Superman Returns added a Superman theme tag to the end of the "As Time Goes By"...