Here are my favorites.
Oh, and some of them may be forgotten favorites not seen for a loooong time.
0: Now I've got 0 in my Bowl. A song where there was different items in a bowl and different animals ate them up. And there's a second version where Miss A.M. Goat appeared at the end of the song to protest in the name of all dairy goats that all goats would eat a pair of sneakers, only to have her efforts frustrated by a pair of other goats munching on some tins.
0: Any sketch with Luis as Señor Zero, a spoof of Zorro.
1: The song sung by Johnny Cash about a western counter who kept counting 1 featuring Big Bird, the Count, and Countess Dahling von Dahling.
1: A pageant where female number Muppets from 10 to 1 counted off backwards so that the number 1 could sing a song at the end. And these female number Muppets had their outlines dotted by small blinking stagelike lightbulbs.
2: Dollhouse, an old live film song about two girls playing with their dolls.
3: The Amazing 3 Song, sung by the cartoon fiddler guy.
4: The classic version of I Just Adore 4 sung by Big Bird and three AM's.
5: The cartoon where a guy finds five apples inside a glass 5 and keeps eating the apples until they keep subtracting and end up in large glass numbers until there are 0 apples.
5: Bat-Five, an old song from SS.
5: The cartoon where five kids keep giving a sick friend five different flowers, until he tells them that he's allergic to flowers.
5: An old live film segment where five showgirls push each other overboard subtracting themselves ending up with 0.
6: Six Snails, a song by the fiddler guy.
7: The Alligator King, the classic version.
8: So many sketches, where to begin! Eight Beautiful Notes, sung by the Count.
Eight Balls fo Fur, sung by Chris of Chris and the Alphabeats.
The Penny Candyman.
The King of Eight.
Lefty Sells Ernie an 8.
Pieces of Eight, where I think it was Paula Poundstone dressed up as a pirate, Big Bird and some kids take a few golden puzzle pieces and place them on the pavement in front of what's now Gina's offices forming a golden 8.
9: The Martian Beauty.
9: Naughty Number Nine, not from SS, it's from School House Rock, but that's one that's always been in the back of my mind from when I had better sight. That cloudy 9 following the unlucky cat like that, major spooky.
9: I'm on Cloud 9, sung by the Count.
10: Ten Tiny Turtles, in it's complete format, is my all-time favorite.
10: Count It Higher, sung by Chris and the Alphabeats.
11: The sketch with the Catherine O'Hara Muppet who gets her entire scene tilted upside-down to show that the 11 drawn on the chalkboard can be read perfectly.
11: The episode with the giant 11.
12: The Ladybug's Picnic is my second all-time favorite.
13: The episode where it keeps storming with thunderclaps everytime Telly says the number 13.
13: Thirteen, You're my Lucky Number, an animated song sung by a cowboy mouse.
14: Fourteen Ducklings were Baked in a Pie.
15: It's Not Easy Being 15.
16: 16 Blues.
17: Number 17 Rap.
18: Eighteen Sandwiches.
19: Number 19 Rap.
20: Whenever any of the counting scenes count up all the way to 20, the best one of these is the one where the numbers are seen in the waters of a Hawaiian isle and they keep changing though I'm not sure if that stopped at 20 or 40. Another classic one is the counting scene that goes up to 20 where the numbers keep getting destroyed or accidentally broken, like when an animated version of Cookie Monster eats the number 14.
21: The Story of Numberella.
21: Ernie's Poem about the number 21.
And finally, the Song of the Count which could count for the number 1!
Oh, and the bird's name is "cuckoo".
Hope this helps and have a good day.