The most tear-jerking Muppet moment...

[DreeRAWRScooter]

Oh yes, I was so sad too when I heard What a Wonderful World sung by Rowlf.

 

[Slackbot]

For me it's the ending of "My Way" in the Lola Falana episode of "The Muppet Show." Gonzo chokes in the middle of the song and turns away from the audience. When Kermit asks what's happening and Gonzo replies that he wants to go there, but he doesn't want to leave here, I get a big lump in his throat. The interplay with Kermit makes me get out my hanky.

For me, that is the saddest moment because it is the most real one, to me at least. No fanfare, no clever words, just heartfelt emotion.

 

[Nekoshema]

A Muppets Christmas Carol [if it's been already mentioned, sorry] when they show Tiny Tim's died. i never cared for Tiny Tim in any version, but it seems as though the sadness stems more from the loss of Jim and Richard and that's what makes it so sad... to me at least, i could just be reading into things

 

[Gonzo's Hobbit]

That part just makes me cry because everyone else is so sad about it, granted when I first saw the movie I was pretty young and didn't know about Jim and Richard dying. Now it's gonna be even more sad. I didn't realize it until I watched it the last time I did but Scrooge tears up in that scene.

 

[lds1987]

To me the most tear jerking moments weren't in the movies, but at Jim Henson's funeral (it's on YouTube...then again everything is on YouTube) when the puppeteers had just finished talking about Jim Henson. Near the end of the funeral it starts as the first puppeteers singing "you are my sunshine" then slowly all the puppeteers over the time since the muppets have started come on the stage, then they bring out all the muppets to sing you are my sunshine, except Kermit who is missing from it all. That really brought it home how much of a hole it would be with out him.

That and when Big Bird came on stage and sang Being Green to the audience, then said everyone on Sesame St would miss Jim.

 

[RedShoebox]

I am not sure why, but the thing that always gets me is the part of Christmas Eve on Sesame Street (is that correct?) in which Bert gives up his paperclips to get a present to give to Ernie, and Ernie gives up Rubber Ducky to get a present to give to Bert. I think it's because I used watch it on VHS all the time, and it brought back tearful memories.

 

[LinkiePie<3]

When I was watching the Sesame Street 35th Anniversary timeline, remembering the old days of Sesame Street....I was hysterically brawling my eyes out :'( <33

 

[DreeRAWRScooter]

I am not sure why, but the thing that always gets me is the part of Christmas Eve on Sesame Street (is that correct?) in which Bert gives up his paperclips to get a present to give to Ernie, and Ernie gives up Rubber Ducky to get a present to give to Bert. I think it's because I used watch it on VHS all the time, and it brought back tearful memories.

Oh I love that one. Good way to teach sharing, no?

 

[LamangoNumber2]

I have a few.
1). Jim Henson Memorial. Scooter, Gobo, Wembley, Elmo, Fozzie, Gonzo, Red, a penguin, Meryl Sheep, Boo Monster, Mokey, Prarie Dawn, Oscar, Telly, Grungetta, and Annie Sue all singing for Jim gets me sobbing.
2). Carol as Big Bird, singing Not Easy Being Green, and litterally, crying inside the suit the whole time, and when he tilts his head, and says 'Thanks, Kermit', I cried like I never did before. I even got the Emotionless people of 4chan to cry to that...
3). The Muppets Celebrate Jim Henson. Another one that made me and the other cold as ice people at 4chan find common ground to mourn our lost leader of Dreams. It really hurts when Fozzie, Gonzo, and Scooter find all the letters... And then Fozzie gives up. Then that one song plays... And when Kermit walks in, everyone sobbed.

 

[MattGallo]

...Carol as Big Bird, singing Not Easy Being Green, and litterally, crying inside the suit the whole time, and when he tilts his head, and says 'Thanks, Kermit', I cried like I never did before...

Agreed.
Also, echoing another common one, Gonzo singing "Back there Someday" from The Muppet Movie (and pretty much anytime Gonzo sings, almoist).
Finally, slightly outside the Muppets, but clearly related, that one guy (Tom Smith?)'s tribute to Jim Henson & Kermit, in song form "A Boy and his Frog", the last line is one of the saddest things I ever encountered, without expecting it to be.