This early skit where Kermit speaks about the letter B. Then Cookie Monster (unnamed at the time) emerges and starts consuming the letter piece by piece. The B turns into an R, then a P, to an F, to a I? A small L? Number 1?, so Kermit tries to keep up with the letter change.
Also in the longer version of this sketch is Kermit's humorous rant about the future Cookie Monster's manners which prompts the monster to come back and apologize... with a big, slobbering, monster kiss on Kermit's face followed by Kermit's patent "Yeesh" face.
A crossover funny moment with The Daily Show: After Jon Stewart pointed out that Grover's harried restaurant customer looked just like Republican Party Chairman Michael Steele, they were able to get that Muppet (or at least a replica) as their own Muppet Michael Steele, responsible for some of the show's best moments.
The Sesame Muppets appearing on talk shows. They tend to get a little more PG-13 when there aren't kids watching.
(Pointing to Stephen's Peabody Award) "Is that cookie?"
At the end of that show, the Award mysteriously disappears as Cookie Monster wipes his lips...
David Rudman performing Cookie Monster on-stage at Ragtag Cinema (one of the few Muppet performances where you can actually see the performer), talking about the media rumor that he's now the Veggie Monster. It evolves into a hilarious monologue in which he first claims "It TRUUUUUE! Yeah! No longer am me going to eat...delicious... crunchy... chocolatey... COOOOKIIIIES!", and then claims to have beat the addiction with a "cookie patch," and briefly renames himself "Brussel Sprout Monster," only to discover he doesn't like brussel sprouts. Finally, he gives up, claims that he'll remain Cookie Monster, even though he will continue to eat other things too: "Me eat, you know... Truck! Bicycle! Fire hydrant! That food group, right?"
The Count's song from the 1975 Bert and Ernie Sing-Along album: "One bat hanging in the steeple/One bat flies in through the door/That makes two bats in my belfry/Wonderful! But wait... there's more!/Two bats hanging in the steeple, etc." ...and then the rest goes on just as you'd expect. Until he gets thrown in the shower.
The ending with Big Bird (who spent the entire special worrying about how Santa would fit down the chimney) sputtering silently after Oscar asks him how the Easter Bunny is able to hide so many eggs in one night is priceless. Cue an "OSCAR!" from the humans.
The entirety of the classic sketch "The Magic Apple" from Sesame Street. Bob is narrating a book that is in turn being performed by Ernie and a couple of other muppets. Fourth-wall violations abound. But this sketch gets especially funny when they trot out a very reluctant Bert in drag, who had to play the part of the princess in the script because no one else was around to do so. "You look great, Bert. You're beautiful!"
The entirety of Bert and Ernie Fish Call. Here Bert and Ernie go fishing is a classic example of Sesame Street's brilliant humor, especially when Ernie's rather unorthodox method of catching fish proves to be far more successful than Bert's more traditional approach.
Grover messing up with the pizza that Mr. Johnson ordered.
Really, any Grover and Mr. Johnson sketch is absolutely hysterical. Particularly if you recall the early sketches, in which Grover was competent but Mr. Johnson was unreasonable - sure, it's just a case of Characterization Marches On, but it's funny to think that Grover's tormenting of his customer for all these decades was in revenge for the events of those first couple of sketches.
ABC Cookie Monster: A little girl sings the alphabet song with Kermit, but every so often, giggling hysterically, she replaces one of the letters with "Cookie Monster". Kermit's reactions are priceless. After the fourth time, Kermit says, "Next time Cookie Monster can do this with you. I'm leaving! Hmmmph!" and storms off. It becomes a Heartwarming Moment when the little girl immediately says, "I love you!" and Kermit comes back on: "I love you, too." And she kisses him.
Oscar was, on the day of Gabi's birth, the only one making regular contact with Luis. Oscar, doubting his honor as a grouch, refuses to tell a soul whether the baby has been born. Bob uses reverse psychology to assure Oscar that he is as grouchy as ever. It doesn't work. Pretty soon, David and Gordon are about ready to kill Oscar. Take a look at this!
Ernie has trouble sleeping, so he tries Counting Sheep, which is visualized to the audience. However, their bleating is so boring that Ernie then moves onto counting fire trucks, which Bert considers too loud, and finally balloons. Ernie imagines blowing up a balloon, which gets so big that it explodes loudly, shaking Bert out of bed, screaming like a girl.
In another nighttime sketch, Ernie left the faucet on after washing his hands before going to bed, which results in a Dripping Disturbance that keeps Bert awake. So Bert sends Ernie to turn it off. But instead of turning off the faucet, Ernie turns on a radio that plays loud music to drown out the dripping (the music heard is quite hilarious in and of itself). Then, instead of turning off the radio, Ernie turns on an even louder vacuum cleaner to drown out the radio. Finally, a frustrated Bert shuts off the racket and then finally settles down into bed for peace and quiet. Alas, Ernie snores as he sleeps!
Bert:(sadly) It's not fair.
In a third nighttime sketch, Ernie wants to know what time it is. But it's too dark to read the clock, so, unable or unwilling to wait until morning, he tries a new method: he leans his head out the window and sings loudly, "O SOLO MIO, O SOLO YOU-O!" This wakes up the whole neighborhood who all yell at him to stop singing because it's 3:00 AM. Satisfied that he knows the time now, Ernie goes back to bed. The whole time, Bert, of course, is not amused.
While no one besides Bert and Ernie is shown on screen, it's implied his singing wakes up the usual human adult cast. Hearing these normally kind individuals yell at Ernie to shut up is hilarious in its own right.
The Hungry Games: Catching Fur has Cookie (as Cookiness Evereat) exclaiming, "Being strong heroine of entire franchise hard work!" and Peeta as... an actual pita. Plus, Cookie's Big "NO!" at the end of the sketch after Finnicky tells him that there's going to be a third "Hungry Games" movie.
Grover and Madeline Kahn performing "Sing After Me" in which Kahn twice vocalizes the "Fiddle-diddle-dee" line. When she starts to do it a third time, Grover turns to her as if to say "Don't you dare!" Kahn proceeds to vocalize the line anyway after Grover sings his part.