To me, Mount Rushmores are about more than just the best. So I've tried to think outside the box a bit.
Danny Carey - Who I think has probably inspired more fledgling drummers than anyone else mentioned in this thread. I was considering Chad Smith here, but Carey doesn't look like Will Ferrell.
Mitch Mitchell - If he hadn't been apart of a glorified backup band sitting behind some guitar player they say was pretty good or whatever, I think he would have become a household name.
Larry Mullen - He is mostly everything Ringo was, but he's stayed at the top of his game for a lot longer - seeing his band go through multiple direction/genre changes.
Phil Collins - Directly responsible for more air drumming than anyone else in the world.
Karen Carpenter - Just because.