Jim Henson wanted the show to end during the peak of its popularity and creativity - and it did. The final year featured the highest Nielsen ratings of its existence.
Initially, the producers had such trouble casting guest stars that they had to call upon their personal friends in the entertainment industry for help. That changed dramatically after Rudolf Nureyev agreed to appear on Rudolf Nureyev (1978)(#2.13). A renowned ballet dancer appearing on such a bizarre show created such a buzz that the show became popular, and soon celebrities were lining up to appear.
Because they found the character so funny, crew members would often crowd into the studio to watch filming skits with the Swedish Chef. Often, the laughter heard in the final sketch is not from a laugh track, but from members of the crew.
Miss Piggy was originally alternately played by Richard Hunt and Frank Oz. As the character grew in popularity, a hesitant Oz took on sole performer status. He once remarked that Piggy was such an intense and over-the-top woman, she could only be played by a man.