Oscar the Grouch Has Never Been Washed 

A little factoid about one of the Oscar puppets that was recently displayed in a museum.
Part of a series of videos made for the MCNY's (now-closed) Puppets of New York exhibit. Shared here with permission.
Some clarifications about the facts presented in this video: It's true that Muppets are rebuilt every few years, largely because the foam structure inside has a tendency to deteriorate from overuse, a phenomenon referred to as "toast." But the fabric will often be recycled on a new build: this is why some puppets have different shapes over the years, but the fur is technically the same as before.
It's worth acknowledging: because of that structure, most of Carroll Spinney's sweat was probably absorbed by the foam, and that gets replaced. So Oscar's fur isn't really that dirty to begin with.