The Nightmare Before Christmas Edit
Oogie's Shadow appears on the moon in the song "This is Halloween".
It was also supposed to be in the "Oogie Boogie's Song" dancing with physical Oogie, but the sequence was taken out of the finished product due to time restraints.
The Nightmare Before Christmas: Oogie's Revenge Edit
The first boss in the game is a shadow-like Oogie Boogie, whom Oogie calls his "mere shadow." After a fight between Jack and the shadow, Boogie escapes. Later, what appears to be the real Oogie Boogie fights with Jack, in his casino, before the foe reveals himself to be Oogie's shadow in disguise. Jack, in this level, destroys the shadow.