My mom and dad always used to love "Batty-Bat".
They also have both immortalized a particular street story that must have been from around 1986 (I was three) in which Elmo is going around showing off his brand new sneakers to everybody, saying over and over "Elmo has new shoes!"
Something about that line and the way Elmo said it struck both my parents very funny, and they've kept it alive ever since. They used to just randomly say it when someone got new shoes
.
The only part of the story I remember is Elmo bugging Maria about the shoes while she's busy with something, and eventually he either trips and falls down out of camera range, or she somehow CAUSES him to fall and smiles in self-satisfaction. (Yeah, I know that second one is unlikely, but that's how I interpreted it as a 3-year-old and that's how I remember it...)
Oh yeah---and my younger sister was always crazy about "Number 9 Cutie" (the Bud Luckey cartoon). We used to sing it.