I've always liked Gonzo because of how misunderstood he was not to mention how he came to be in real life thanks in part to his creator/puppeteer, Dave Goelz.
Statler and Waldorf are also favourites because of their heckling. Sure, their shtick is close to 50 years old, yet they continue coming up with new material due to changes in culture and the like.
Of course, I can't ignore Kermit, the straight man of the Muppets, and their de facto leader.