Lullaby On Broadway. That penguin kills me.
This one is my favorite, for sentimental reasons. I’m just the right age to have enjoyed the Muppet Show as a kid (first-run!) and my late father used to just burst into this song at random times for years. I always think of him when I hear it.
Frankly, this is destined to be one of the greatest threads ever on the Dope.
My contribution is Danny Boy.
ETA:
I can’t stop laughing at this one!
Nobody yet has mentioned the Land of Skorch and Skred?
Oops. Did I do that right?
The link you did correctly. But it was the Land of Gorch. And the character’s name was Scred.
Harry Belafonte’s first performance of “The Banana Boat Song” on TV:
Fozzie: Trust me
Harry Belafonte: That’s what you said the last time.
The Rodger Moore Spy Epic, “Talk To The Animals”
Everything Zero Mostel said backstage.
My favorite Swedish Chef sketch was when he was trying to cook spaghetti, and the mass of spaghetti kept trying to get away.
Mikhail Baryshnikov dancing “Swine Lake”. (And all of Sam the Eagle’s appearances in that episode.)
Vincent Price, Sweetums, Uncle Deadly, and the rest of the “scary monster” muppets singing “You’ve Got A Friend”.
Just about any “Veterinarian’s Hospital” sketch. I loved all the terrible puns.
Here is a good example.
One of my favorites is Pig Calypso.
Are episodes of the Muppet Show available on DVD?
The chickens clucking/singing “Baby Face.”
But my favourite muppet character is Animal & he & Rita Moreno duetting on “Fever” deserves an honourable mention.
I used to have a neat link that had all (16?) episodes plot, script, and backstage notes from SNL, but I can’t find it anymore. It was really neat. It gave the muppets “off-stage” personalities and interaction.
Still, I thought those ugly bastards were the funniest thing on TV at the time. But I was only a kid, so that’s FWIW.
A big improvement on the original. I’ll have to keep thinking about the best sketch - most of my favorite moments are in the movies.
Oh man, I love this thread. The Muppet Show was pure genius, and I loved every minute of it as a kid AND as an adult. I love that there are so many things on the show that would never be considered “appropriate” children’s programming now. And that’s just the thing, TMS was not a children’s show. It was a prime time variety show for everyone.
But before I write an ode to Kermie, I will first give you…Mahna Mahna:
And my all time favorite Gonzo (accompanied by Rowlf) performance of Nobody…it’s just so Gonzo, lol:
It’s hard to name favorites, but if I had to it would be anything with Dr. Teeth and the Electric Mayhem—Animal, Floyd, Janis…COME ON! They were beyond cool.
Wild Thing–Animal
And, of course, TMS had the BEST guests. Anybody who was anybody went on The Muppet Show!
Welcome to my Nightmare–Alice Cooper w Muppets
The Rita Moreno bit is one of my favorites too!
Especially in the first season, before the show earned a certain cachet, I noticed even as a kid that the guests skewed heavily toward European performers. I didn’t realize until much later that this was because the show was filmed in England!
Hmm, here’s a list of the guest stars from Season 1. They definitely do not skew heavily toward European performers.
Juliet Prowse
Connie Stevens
Joel Gray
Ruth Buzzi
Rita Moreno
Jim Neighbors
Florence Henderson
Paul Williams
Charles Aznavor
Harvey Korman
Lena Horne
Peter Ustinov
Bruce Forsyth
Sandy Duncan
Candice Bergen
Avery Shriever
Ben Vereen
Phyllis Diller
Vincent Price
Valerie Harper
Twiggy
Ethel Merman and Ray Bradshaw
Kaye Ballard
Mummenschanz
I am nothing if not obsessive about The Muppet Show. 
Yeah, my impressions appear to be inaccurate. There ARE four European performers in there…(well, if you count Mummenshanz as one performer).