It’s been years since I’ve seen the show, but my favorite song to this day is, “I Don’t Want to Live on the Moon.” It’s crazy at my age, but that song still does something for me.
Said the alligator king to his seven sons
“I’m feelin’ mighty down
whichever one of you can cheer me up
will wear my royal crown”
Always my favourite and I still get it stuck in my head 
Rubber ducky, you’re the one!
You make bath time so much fun.
Rubber ducky, you’re my very best friend, it’s true…
That’s the closest one for me. Sesame Street was after my time and we never had kids so most of that missed me. But that one I remember getting a lot of radio play for a few months way back when.
“I Don’t Want to Live on the Moon” is a good choice; I’ll second that and add “Dance Myself to Sleep” and the song that plays during the “1-2-3 Red Ball” sequence. I hum the latter whenever I see the Rube Goldberg machine at the beginning of Elementary.
“It is I, Captain Vegetable
With my carrots and my celery…”
Oooh, thanks for sharing that one; just watched it for the first time!
*Oh, everything comes in its own special size,
Guess it can be measured by where you put your eyes.
It’s so big when you’re close; it looks smaller back a bit.
And that’s about the size of it.
That’s about the size; where you put your eyes.
That’s about the size of it.*
Very catchy in a most pleasant way, with a message about perspective that’s surprisingly deep for a kids’ show.
We all live in a Capital I
In the middle of a desert
In the center of the sky
When we were kids my sister used to LOVE “Me and My Llama”.
(Fuck, now I’m looking up old Sesame Street songs on youtube. We all sing with the same voice the same song, the same voice, we all sing with the same voice and we sing in harmony!)
Sunny day
Chasing the clouds away
On my way
To where the air is sweet!
Can you tell me how to find, how to find Cafe Society!!!
One of these things is not like the others.
One of these things is not the same.
We still use that one.
Now, in terms of top 40 songs that had a version done on Sesame Street, I’ve always been partial to Shiny, Happy Monsters by REM. 
Put Down the Duckie (if you want to play the saxophone!)
Yes, hard to top the theme song, sweet memories for me!
So surreal.
Beat me to it! 1-2-3-4-5-6-7-8-9-10-11-12 is funkay.
Ab-kadefky-jeckle-ma-nop-kwur-stoove-wix-is!
Your hands can do so many different things:
brush your teeth or comb your hair,
throw a ball into the air,
wave hello or wave goodbye,
even make a pizza pie!
So many things your hands can do!
Sung in The Count’s voice, of course!
I’ve always liked the version of the theme in MAD Magazine:
Crummy day, smoggy sky’s charcoal grey!
On my way past where the bullies meet!
Can you tell me how to avoid, how to avoid
Reality Street?
Ooooooh!!! Remember the take they did on nuclear war and the number five?
Five countries with five nuclear warheads.
Five world leaders with five different opinions.
Five panic buttons with five fingers.
Five Easy Pieces. (The Earth explodes into five big chunks.)
Mad Magazine was DA bomb!
The same composer/singer (Steve Zuckerman) did the similarly awesome Lowercase n.
There was also a short “How It’s Made” type video set in a crayon factory that had a cool little prog-ish instrumental soundtrack. Apparently a blend of two songs, Water Course A and Exchange by Richard Harvey.
Sing makes me cry. I used to sing it to my kids when I changed their diapers.