How awesome was that song? Statler and Waldorf didn't even snark at it. Instead they joined in.
Gonzo actually performed his trumpet correctly.
This performance was so beloved by Henson that Belafonte performed the song at his funeral.
In the fifth season episode with Marty Feldman, they had an awesome song "A Hot Time in the Old Town Tonight". During the song, a good number of Sesame Street characters come out and sing their theme with Fozzie and the others joining, then another verse of "Hot Time". To top it all off, the song featured Fozzie, Cookie Monster, Grover, and Bert singing. All of them are voiced by Frank Oz (and usually puppetered, although that obviously wasn't a possibility for this). That meant Frank Oz had to sing at least a portion of the musical number four times. See it here.
Animal, the most manic Muppet ever, tires out and Buddy continues playing for an entire minute afterwards, to Animal's goggle-eyed shock.
When Kermit found out Miss Piggy planted a false story about them getting married in Vegas, Kermit snaps at Piggy, and fires her. (Guest star Loretta Swit briefly took over Piggy's roles on Veterinarian's Hospital and Pigs In Space.) Yeah, Piggy gets rehired in the end but still, after five seasons of having to put up crap from Piggy and the other assorted madness behind the scenes, seeing him getting pissed and yelling at the top of the lungs was a sight to behold.
Rudolph Nureyev's appearance. During the show's first season, they had a lot of trouble getting celebrities to appear on the show and often had to appeal to personal favors. Then Nureyev actually approached Henson and asked if he could appear, and suddenly made that job a whole lot easier. For himself, Rudolph really got to shine not only in ballet, but also paying tribute to Fred Astaire with a superb tap song and dance number of "Top Hat, White Tie and Tails".
Plus his partner in "Swine Lake", who's able to keep up with one of the greatest ballet dancers ever while wearing a very bulky costume.
Candice Bergen plays a frontier wife whose husband keeps demanding she do various chores while he just sits by the fire. Suddenly she swaps her clothes for a girl power outfit and threatens him with a shotgun before shooting her way out the door.
The epic pirate battle at the end of the Glenda Jackson episode.
In the Connie Stevens episode, Ernie and Bert guest star. Bert is nervous, Ernie tries to trick him into making a fool of himself. The result is Bert belting out "Some Enchanted Evening" and dancing with Connie Stevens. Seeing Ernie's reaction as his prank fails magnificently sells the whole thing. (Though he still gets one last dig at Bert in the end.) See it here.
Most fans will admit that seeing Beaker finally getting back at Bunsen and chasing him around the theater with his many, many clones in the Mac Davis episode was pretty awesome and much-deserved.
Alice Cooper's perfect response to Sam accusing him of being a sick weirdo. "Thank you!", then tallying up with his finger "One for my side!"
Rich Little does a takeoff on Fozzie, to which Waldorf and Statler say he's too funny for it to be a good impression. He retaliates by doing an impression of them.
In the George Burns episode, George handles Fleet Scribbler, a gossip column writer who, as Kermit says, will do anything for sensationalism, in truly epic fashion, using each question to segue into a joke.
An awesome moment for the production team; during the Brooke Shields episode, in which the whole half-hour was devoted to Alice in Wonderland, they designed an original Jabberwock Muppet for a recitation of "Jabberwocky" which looked almost exactly like John Tenniel's original illustrations.