I'd have to go with Floyd. Why? Three reasons. First, his look. Especially as the years went on, he just looked more and more human and less puppet-like. He was so human when he would close his eyes and laugh. Second, his singing. He was, by far, the best singer out of the Muppet Show, next to Scooter and Kermit. And third, his personality. He just seemed to be more mature and adult-like than any other character. He was just more loose about himself and definitely more daring.
"We gonna have a swell time, me and little puppy Foo Foo here. We got the brush to brush, the coat to keep her warm, the spoon to feed her. And a nice safe place to keep the little puppy dog. Breathe thru the key hole, Turkey Dog!"