Just about all my favorites were from Season 1 (I loved Ernie's shirt).
A lot of them have been posted on youtube for your viewing pleasure. But a few really stand out:
Ernie, the World's Greatest Counter, finally counts to 10 after many distractions (and torturing Bert in the process), and starts to recite the alphabet, causing Bert to have the mother of all freakouts. (The last ten seconds have been cut off the Old School box set, but someone tacked on the missing footage on youtube. Great stuff despite the poor dubbing.
Ernie eats Bert's chocolate cake, then tries to cover up his mistake by spinning a tall tale of a monster eating the cake on him. "You know how monsters like cake, Bert!" Then Beautiful Day shows up, eats the other piece of cake Bert was saving, and Bert ain't buying Ernie's excuses anymore.
Best of all (maybe someday we'll see it again) Bert wanted Ernie to get a newspaper from Hooper's Store, and Ernie arms himself with a flashlight, umbrella, and raincoat to make the perilous journey across the street. Unfortunately he doesn't have any bubble gum to ward off any bears. Ernie's logic:"If you give a bear some bubble gum, he'll be too busy chewing it to bite you!" Bert throws up his hands and agrees to go to Hooper's to get some bubble gum for Ernie. Then Ernie delivers the punchline: "Hey,Bert, while you're there, can you pick up a newspaper?" Which sends Bert into another state of hysteria..
This is another one of my Holy Grails I hope will see daylight again someday.