This Funny Faces puzzle from the 1950s features great characters, and is actually a lot of fun to play around with. Each character is die cut into sections that can be switched and rearranged to make "more than 1000 different faces!" I haven't actually tested that claim, as I imagine it would require more time than I can realistically spend playing with my toys.
The original four characters:
The illustrations remind me of those on Changeable Charlie, another vintage make-a-face toy.