Harvey
Actually, Jim henson often performed harvey Monster, the dark blue monster with black eyebrows, big orange (I coudl be wrong about the color) nose, and yellow horns, seen in the songs "We're all monsters", "fur", and "ABC Disco" (where he was performed by Richard Hunt). he also appeared in the Monsterpiece Theatre segment "Me, Claudius".
Richard Hunt also had a few monster characters, but his most major monster character, Two-headed Monster, was shared with Jerry Nelson. His other regular monster characters, Leo and Aristotle, didn't last very long (I think they both only lasted one year each), and of course we all know how he didn't like to perform Elmo.