It's hard for me to explain - or even pin down - what it is about Scooter that makes him my favorite character. I like how he seems to be an observer to the madness that is the Muppet Show; sometimes he gets his chance onstage, either as part of the chorus or else in his own spot, but most of the time Scooter stays backstage hanging out and taking care of various backstage necessities for Kermit.
I like Scooter's enthusiasm, so much of which was Richard Hunt's own enthusiasm. He was so excited to be a part of the Muppet Show that he didn't mind just being a go-fer. Even though Scooter would frequently drop his uncle's name in order to secure a spot on the show, or else do something that Kermit didn't especially want done, he never used his uncle's influence to get higher in the backstage hierarchy. He was content to be a go-fer. Scooter also wasn't above using his own smarts to get things done; for instance in the Sylvester Stallone episode instead of using his uncle to convince Kermit to let Sly's groupies backstage, Scooter convinced the girls to pretend that they were there to see Kermit instead.
To sum it up, I like Scooter because he seems, in the middle of all the lunacy that is the Muppet Show, like a normal kid (or as normal as the Muppets get).
-Kim