There are just too many great duos on the Muppet show to choose just one. And let's not forget dous on other projects. Sesame Street, Fraggle Rock, even Dinosuars has great duo moments (Earl and B.P, Earl and Ethel, Earl and Baby... Mostly Earl and someone else... and Robbie and Spike).
But I have to say, my favorite duo would be Statler and Waldorf. What drives them? Why do they always show up? Do they get a thrill out of heckling? Do they make people feel small on purpose, or do they just like to complain about things, like other grouchy old men?
In a close second place, Bunsen and Beaker. Now, like almost every duo, it follows Jim's original comedic intentions. One short stubby guy, one uptight tall thin guy. much like Ernie and Bert... but Ernie is more sadistic, and Beaker's uptightness stems from fear of whatever Bunsen has up his sleeve. Bunsen clearly isn't in it for the amuzement of having Beaker get blown up. he really feels that he is making the world a better place. And something tells me Beaker feels that way too.